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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1-15 
    ISSN: 0271-2091
    Keywords: shallow water equations ; boundary element method ; wave equation model ; free surface flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The present paper makes use of a wave equation formulation of the primitive shallow water equations to simulate one-dimensional free surface flow. A numerical formulation of the boundary element method is then developed to solve the wave continuity equation using a time-dependent fundamental solution, while an explicit finite difference scheme is used to derive velocities from the primitive momentum equation. One-dimensional free surface flows in open channels are treated and the results compared with analytical and numerical solutions. © 1997 John Wiley & Sons, Ltd.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 81-100 
    ISSN: 0271-2091
    Keywords: boundary element ; velocity ; gradients ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The direct boundary element method is an excellent candidate for imposing the normal flux boundary condition in vortex simulation of the three-dimensional Navier-Stokes equations. For internal flows, the Neumann problem governing the velocity potential that imposes the correct normal flux is ill-posed and, in the discrete form, yields a singular matrix. Current approaches for removing the singularity yield unacceptable results for the velocity and its gradients. A new approach is suggested based on the introduction of a pseudo-Lagrange multiplier, which redistributes localized discretization errors - endemic to collocation techniques -  over the entire domain surface, and is shown to yield excellent results. Additionally, a regularized integral formulation for the velocity gradients is developed which reduces the order of the integrand singularity from four to two. This new formulation is necessary for the accurate evaluation of vorticity stretch, especially as the evaluation points approach the boundaries. Moreover, to guarantee second-order differentiability of the boundary potential distribution, a piecewise quadratic variation in the potential is assumed over triangular boundary elements. Two independent node-numbering systems are assigned to the potential and normal flux distribu- tions on the boundary to account for the single- and multi-valuedness of these variables, respectively. As a result, higher accuracy as well as significantly reduced memory and computational cost is achieved for the solution of the Neumann problem. © 1997 John Wiley & Sons, Ltd.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 101-120 
    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; adaptive FEM ; turbulencek-∊ model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents an adaptive finite element method for solving incompressible turbulent flows using a k-∊ model of turbulence. Solutions are obtained in primitive variables using a highly accurate quadratic finite element on unstructured grids. A projection error estimator is presented that takes into account the relative importance of the errors in velocity, pressure and turbulence variables. The efficiency and convergence rate of the methodology are evaluated by solving problems with known analytical solutions. The method is then applied to turbulent flow over a backward-facing step and predictions are compared with experimental measurements. © 1997 John Wiley & Sons, Ltd.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 127-139 
    ISSN: 0271-2091
    Keywords: semi-Lagrangian ; advection ; accuracy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes a technique for achieving accurate numerical simulations of advective transport at large Courant numbers using large time steps. The scheme is called ULTIMATE DISCUS and it implements Leonard's universal flux limiter and QUICKEST algorithms within a semi- Lagrangian treatment of advection. This enables the scheme to achieve monotonic solutions, mass conservation and, most importantly, high accuracy without any limit on the time step (or Courant number).The results of numerical experiments of advection over a fixed distance show that the accuracy of the method increases with increasing spatial resolution and generally increases (but in a non-trivial manner) with increasing Courant number. Accuracy is exact at all integer values of Courant number; for Courant numbers increasing between zero and one, accuracy improves rapidly and monotonically; for other integer-integer ranges of Courant number there is a minimum of accuracy close to the mid-range value. This behaviour is explained in terms of the known accuracy of the QUICKSET algorithm as a function of Courant number and the reducing number of interpolative steps required in the simulations as the Courant number increases. The use of the flux limiter is shown to remove non-physical oscillations from the solution, but at the price of a few per cent reduction in global accuracy caused by increased suppression of peak values. © 1997 by John Wiley & Sons, Ltd.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 141-153 
    ISSN: 0271-2091
    Keywords: finite element ; non-oscillatory ; strong discontinuity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A non-oscillatory no-free-parameter finite element method (NNFEM) is presented based on the consideration of wave propagation characteristic in different characteristic directions across a strong discontinuity through flux vector splitting in order to satisfy the increasing entropy condition. The algorithm is analysed in detail for the one-dimensional (1D) Euler equation and then extended to the 2D, axisymmetric and 3D Euler and Navier-Stokes equations. Its applications in various cases - in viscid oblique shock wave reflection, flow over a forward step, axisymmetric free jet flow, supersonic flows over 2D and 3D rectangular cavities - are given. These computational results show that the present NNFEM is efficient in practice and stable in operations and is especially capable of giving good resolution in simulating complicated separated and vortical flows interacting with shock waves. © 1997 by John Wiley & Sons, Ltd.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 169-183 
    ISSN: 0271-2091
    Keywords: convection-dominated diffusion equations ; TVD schemes ; antidiffusive schemes ; flux limiter scheme ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Approximating convection-dominated diffusion equations requires a very accurate scheme for the convection term. The most famous is the method of backward characteristics, which is very precise when a good interpolation procedure is used. However, this method is difficult to implement in 2D or 3D. The goal of this paper is to show that it is possible to construct finite difference schemes almost as accurate as the method of characteristics. Starting from a family of second- and third- order Lax-Wendroff-type schemes, a TVD and L∞- stable scheme that is easy to implement in higher dimensions is constructed. Numerical tests are performed on various model problems whose solution is known and on classical problems. Comparisons with some other limiter schemes and the method of characteristics are discussed. © 1997 by John Wiley & Sons, Ltd.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 17-59 
    ISSN: 0271-2091
    Keywords: radiation boundary condition ; numerical model ; coastal upwelling ; baroclinic model ; coastal jet ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-dimensional baroclinic model is described for coastal upwelling in a vertical plane perpendicular to the coast. The model consists of equations of motion, continuity and turbulence energy along with equations for salinity and thermal energy and an equation of state. The role of density gradient in the baroclinic pressure gradient is investigated to understand the dynamics during the upwelling process. To represent the surface and bottom boundaries corresponding to a fixed computational level in the discretized equations, a set of non-dimensional co-ordinates is used. These co-ordinates are then transformed onto logarithmic co-ordinate axes to resolve effectively the boundary layers.The first experiment is carried out with a flat bottom to understand the dynamics of the upwelling and the structural features of the process by diagnostic analysis of the balance between various terms of the momentum equation. Starting from a state of rest, a spatially uniform alongshore wind stress corresponding to the mean monthly wind stress for the month of May is applied and held constant thereafter. The fluid is assumed to be incompressible and stratified, with the initial temperature and salinity having no horizontal variations but a uniform vertical gradient. As the upwelling phenomenon is transient in nature and keeping in mind the additional computational overheads, the response of the model is studied day-wise up to 4 days.In the second experiment the model is applied to study the upwelling off the east coast of India in a plane normal to the coast of Visakhapatnam. The analysis area extends to 100 km offshore with real topography. The results are presented day-wise for 4 days, comparing the balance between various terms in the upwelling region and in the open sea, and the dynamics of the baroclinic coastal jet is explained. © 1997 John Wiley & Sons, Ltd.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 215-232 
    ISSN: 0271-2091
    Keywords: PDF method ; turbulent flow ; wall treatment ; pressure algorithm ; Monte Carlo method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The generalized Langevin model, which is used to model the motion of stochastic particles in the velocity-composition joint probability density function (PDF) method for reacting turbulent flows, has been extended to incorporate solid wall effects. Anisotropy of Reynolds stresses in the near-wall region has been addressed. Numerical experiments have been performed to demonstrate that the forces in the near-wall region of a turbulent flow cause the stochastic particles approachi ng a solid wall to reverse their direction of motion normal to the wall and thereby, leave the near-wall layer. This new boundary treatment has subsequently been implemented in a full-scale problem to prove its validity. The test problem considered here is that of an isothermal, non-reacting turbulent flow in a two-dimensional channel with plug inflow and a fixed back-pressure. An efficient pressure correction method, developed in the spirit of the PISO algorithm, has been implemented. The pressure correction strategy is easy to implement and is completely consistent with the time- marching scheme used for the solution of the Lagrangian momentum equations. The results show remarkable agreement with both k-∊ and algebraic Reynolds stress model calculations for the primary velocity. The secondary flow velocity and the turbulent moments are in better agreement with the algebraic Reynolds stress model predictions than the k- ∊ predictions. © 1997 by John Wiley & Sons, Ltd.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 441-455 
    ISSN: 0271-2091
    Keywords: finite elements ; Richards equation ; porous flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new computational method is developed for numerical solution of the Richards equation for flow in variably saturated porous media. The new method, referred to as the mixed transform finite element method, employs the mixed formulation of the Richards equation but expressed in terms of a partitioned transform. An iterative finite element algorithm is derived using a Newton-Galerkin weak statement. Specific advantages of the new method are demonstrated with applications to a set of one- dimensional test problems. Comparisons with the modified Picard method show that the new method produces more robust solutions for a broad range of soil- moisture regimes, including flow in desiccated soils, in heterogeneous media and in layered soils with formation of perched water zones. In addition, the mixed transform finite element method is shown to converge faster than the modified Picard method in a number of cases and to accurately represent pressure head and moisture content profiles with very steep fronts. © 1997 by John Wiley & Sons, Ltd.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 493-517 
    ISSN: 0271-2091
    Keywords: viscoelasticity ; Leonov model ; entrance flow ; upwind scheme ; polymer ; rheology ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A simulation of planar 2D flow of a viscoelastic fluid employing the Leonov constitutive equation has been presented. Triangular finite elements with lower-order interpolations have been employed for velocity and pressure as well as the extra stress tensor arising from the constitutive equation. A generalized Lesaint-Raviart method has been used for an upwind discretization of the material derivative of the extra stress tensor in the constitutive equation. The upwind scheme has been further strengthened in our code by also introducing a non-consistent streamline upwind Petrov-Galerkin method to modify the weighting function of the material derivative term in the variational form of the constitutive equation. A variational equation for configurational incompressibility of the Leonov model has also been satisfied explicitly.The corresponding software has been used to simulate planar 2D entrance flow for a 4:1 abrupt contraction up to a Deborah number of 670 (Weissenberg number of 6·71) for a rubber compound using a three-mode Leonov model. The predicted entrance loss is found to be in good agreement with experimental results from the literature. Corresponding comparisons for a commercial-grade polystyrene, however, indicate that the predicted entrance loss is low by a factor of about four, indicating a need for further investigation. © 1997 by John Wiley & Sons, Ltd.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 519-530 
    ISSN: 0271-2091
    Keywords: local mesh refinement ; multigrid ; finite volume ; SIMPLEC ; k-∊ ; buoyancy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a local mesh refinement procedure based on a discretization over internal interfaces where the averaging is performed on the coarse side. It is implemented in a multigrid environment but can optionally be used without it. The discretization for the convective terms in the velocity and the temperature equation is the QUICK scheme, while the HYBRID-UPWIND scheme is used in the turbulence equations. The turbulence model used is a two-layer k-∊ model. We have applied this formulation on a backward-facing step at Re=800 and on a three-dimensional turbulent ventilated enclosure, where we have resolved a geometrically complex inlet consisting of 84 nozzles. In both cases the concept of local mesh refinements was found to be an efficient and accurate solution strategy. © 1997 by John Wiley & Sons, Ltd.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 537-561 
    ISSN: 0271-2091
    Keywords: third-order upwinding ; numerical diffusion ; numerical instabilities ; dye transport ; sedimentation tank ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new numerical model has been developed to simulate the transport of dye in primary sedimentation tanks operating under neutral density conditions. A multidimensional algorithm based on a new skew third-order upwinding scheme (STOUS) is used to eliminate numerical diffusion. This algorithm introduces cross-difference terms to overcome the instability problems of the componentwise one-dimensional formulae for simulating multi-dimensional flows. Small physically unrealistic overshooting and undershooting have been avoided by using a well-established technique known as the universal limiter. A well-known rotating velocity field test was used to show the capability of STOUS in eliminating numerical diffusion. The STOUS results are compared with another third-order upwinding technique known as UTOPIA. The velocity field is obtained by solving the equations of motion in the vorticity-streamfunction formulation. A k- ∊ model is used to simulate the turbulence phenomena. The velocity field compares favourably with previous measurements and with UTOPIA results. An additional differential equation governing the unsteady transport of dye in a steady flow field is solved to calculate the dye concentration and to produce flow-through curves (FTCs) which are used in evaluating the hydraulic efficiency of settling tanks. The resulting FTC was compared with both measurements and numerical results predicted by various discretization schemes. © 1997 by John Wiley & Sons, Ltd.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 579-593 
    ISSN: 0271-2091
    Keywords: Eulerian-Lagrange computation ; bubbly flow ; void fraction distribution ; two-fluid model ; gas-liquid flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A comprehensively theoretical model is developed and numerically solved to investigate the phase distribution phenomena in a two-dimensional, axisymmetric, developing, two-phase bubbly flow. The Eulerian approach treats the fluid phase as a continuum and solved Eulerian conservation equations for the liquid phase. The Lagrangian bubbles are tracked by solving the equation of motion for the gas phase. The interphase momentum changes are included in the equations. The numerical model successfully predicts detailed flow velocity profiles for both liquid and gas phases. The development of the wall-peaking phenomenon of the void fraction and velocity profiles is also characterized for the developing flow. For 42 experiments in which the mean void fraction is less than 20 per cent, numerical calculations demonstrate that the predictions agree well with Liu's experimental data. © 1997 by John Wiley & Sons, Ltd.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 615-638 
    ISSN: 0271-2091
    Keywords: finite element method ; front tracking ; incompressible two fluid system ; mold filling ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model has been developed for the 2D simulation of free surface flows or, more generally speaking, moving interface ones. The bulk fluids on both sides of the interface are taken into account in simulating the incompressible laminar flow state. In the case of heat transfer the whole system, i.e. walls as well as possible obstacles, is considered. This model is based on finite element analysis with an Eulerian approach and an unstructured fixed mesh. A special technique to localize the interface allows its temporal evolution through this mesh. Several numerical examples are presented to demonstrate the capabilities of the model. © 1997 by John Wiley & Sons, Ltd.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 645-670 
    ISSN: 0271-2091
    Keywords: hydraulic fracturing ; finite elements ; moving adaptive grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A mathematical model and adaptive finite element scheme are developed for describing the distribution of proppant in a propagating hydraulic fracture. The governing equation for proppant concentration is derived by applying the conservation law of mass to the proppant and to the proppant-laden fluid. Shah's empirical equation, which relates the proppant concentration and the indices of the non-Newtonian fluid, is used to describe the proppant-laden fluid. The proppant distribution inside a hydraulic fracture can then be obtained by solving the proppant concentration equation together with the governing equations of fluid and elasticity for a hydraulic fracturing. A novel moving grid scheme is developed that combines grid point insertion with redistribution. Four examples corresponding to different in situ stress distributions are computed to demonstrate the scheme. © 1997 by John Wiley & Sons, Ltd.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 693-714 
    ISSN: 0271-2091
    Keywords: finite element ; turbulence ; algebraic stress model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes a finite element numerical model for the simulation of both steady and truly transient turbulent flow in two dimensions. All elements of the model and computational approach were chosen, however, for ease of applicability in the future to fully three-dimensional flows. The turbulent mean flow is described by the Reynolds- averaged Navier-Stokes equations. The well-known two-equation K-ε model is the base for the representation of turbulence quantities. From three candidate algebraic stress models, Rodi's model was chosen for implementation after preliminary tests on turbulent channel flow. The scheme was then tested at length on flow past a backward-facing step and flow past a box. Comparisons were made with the computed and experimental results of other investigators. For the backward-facing step problem the model appears to equal or improve upon the accuracy of prediction s of earlier finite element codes. The frequency of vortex shedding from the corners of the box in terms of the Strouhal number is predicted well. © 1997 by John Wiley & Sons, Ltd.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 739-757 
    ISSN: 0271-2091
    Keywords: numerical analysis ; boundary conditions ; aeroelasticity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper analyses the accuracy and numerical stability of coupling procedures in aeroelastic modelling. A two-dimensional model problem assuming unsteady inviscid flow past an oscillating wall leads to an even simpler one-dimensional model problem. Analysis of different numerical algorithms shows that in general the coupling procedures are numerically stable, but care is required to achieve accuracy when using very few time steps per period of natural oscillation of the structure. The relevance of the analysis to fully three-dimensional applications is discussed. © 1997 by John Wiley & Sons, Ltd.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 863-873 
    ISSN: 0271-2091
    Keywords: general BEM ; general non-linear differential operator ; homotopy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the general BEM proposed previously by Liao is applied to solve some 2D strongly non-linear differential equations, even including those whose governing equations and boundary conditions do not contain any linear terms. It is shown that the proposed general BEM is really valid for general non-linear problems, so that it can be applied to solve high-dimensional, strongly non-linear problems in engineering. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 863-873, 1997.
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  • 19
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 337-349 
    ISSN: 0271-2091
    Keywords: Oldroyd-B ; non-Newtonian ; boundary layer ; collocation ; spline ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The steady flow of an Oldroyd-B fluid between two porous concentric circular cylinders is studied. The equation of motion and the constitutive equations form a system of non-linear ODEs that is solved numerically, and in a few cases the numerical results are compared with a known analytical solution. We consider the effect of the non-Newtonian nature of the fluid on the drag and on the boundary layer structure near the walls. Numerical computations show the effect of the non-Newtonian quantities on the velocity and on the shear stress as the dimensionless parameters are varied. © by 1997 John Wiley & Sons, Ltd.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 563-578 
    ISSN: 0271-2091
    Keywords: Burgers equation ; Green element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The transient one-dimensional Burgers equation is solved by a mixed formulation of the Green element method (GEM) which is based essentially on the singular integral theory of the boundary element method (BEM). The GEM employs the fundamental solution of the term with the highest derivative to construct a system of discrete first-order non- linear equations in terms of the primary variable, the velocity, and its spatial derivative which are solved by a two-level generalized and a modified time discretization scheme and by the Newton-Raphson algorithm. We found that the two-level scheme with a weight of 0ċ67 and the modified fully implicit scheme with a weight of 1ċ5 offered some marginal gains in accuracy. Three numerical examples which cover a wide range of flow regimes are used to demonstrate the capabilities of the present formulation. Improvement of the present formulation over an earlier BE formulation which uses a linearized operator of the differential equation is demonstrated. © 1997 by John Wiley & Sons, Ltd.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 595-613 
    ISSN: 0271-2091
    Keywords: advection-diffusion equation ; discontinuous finite element method ; mixed finite element method ; solute transport in porous media ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: When transport is advection-dominated, classical numerical methods introduce excessive artificial diffusion and spurious oscillations. Special methods are required to overcome these phenomena. To solve the advection-diffusion equation, a numerical method is developed using a discontinuous finite element method for the discretization of the advective terms. At the discontinuities of the approximate solution, numerical advective fluxes are calculated using one-dimensional approximate Riemann solvers. The method is stabilized with a multidimensional slope limiter which introduces small amounts of numerical diffusion when sharp concentration fronts occur. In addition, the diffusive term is discretized using a mixed hybrid finite element method. With this approach, numerical oscillations are completely avoided for a full range of cell Peclet numbers. The combination of discontinuous and mixed finite elements can be easily applied to 2D and 3D models using various types of elements in regular and irregular meshes. Numerical tests show good agreement with 1D and 2D analytical solutions. This approach is compared at the same time with two different numerical methods, a standard mixed finite method and a finite volume approach with high-resolution upwind terms. Regular and irregular meshes are used for the numerical tests to study the mesh effects on the numerical results. Our data show that in all cases this approach performs well. © 1997 by John Wiley & Sons, Ltd.
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  • 22
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 671-691 
    ISSN: 0271-2091
    Keywords: volume tracking ; interfacial flow ; flux-corrected transport ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new algorithm for volume tracking which is based on the concept of flux-corrected transport (FCT) is introduced. It is applicable to incompressible 2D flow simulations on finite volume and difference meshes. The method requires no explicit interface reconstruction, is direction-split and can be extended to 3D and orthogonal curvilinear meshes in a straightforward manner. A comparison of the new scheme against well-known existing 2D finite volume techniques is undertaken. A series of progressively more difficult advection tests is used to test the accuracy of each scheme and it is seen that simple advection tests are inadequate indicators of the performance of volume-tracking methods. A straightforward methodology is presented that allows more rigorous estimates to be made of the error in volume advection and coupled volume and momentum advection in real flow situations. The volume advection schemes are put to a final test in the case of Rayleigh-Taylor instability. © 1997 by CSIRO.
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  • 23
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 715-734 
    ISSN: 0271-2091
    Keywords: incompressible Navier-Stokes ; finite difference schemes ; GMRES ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present new finite difference schemes for the incompressible Navier-Stokes equations. The schemes are based on two spatial differencing methods; one is fourth-order-accurate and the other is sixth-order accurate. The temporal differencing is based on backward differencing formulae. The schemes use non-staggered grids and satisfy regularity estimates, guaranteeing smoothness of the solutions. The schemes are computationally efficient. Computational results demonstrating the accuracy are presented. © 1997 by John Wiley & Sons, Ltd.
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  • 24
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 787-806 
    ISSN: 0271-2091
    Keywords: three-dimensional ; two-phase flow ; Eulerian modelling ; RNG k-∊ turbulence model ; particle-wall collision ; power utility boilers ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-fluid Eulerian model in combination with a particle-wall collision model and generalized Eulerian boundary conditions for the particulate phase is employed to predict complex three- dimensional fly-ash flows which often cause severe erosion to boiler tubes located in power utility boilers. Mean momentum and mass conservation equations are solved for each phase using a finite volume scheme with two-way coupling and a modified renormalization group (RNG)-based k -∊ turbulence model. Comparison of predicted particle concentration with measured data is made and excellent agreement is obtained. The detailed character of the particulate velocity field and concentration just downstream of the 180° bend shows a marked dependence on the Stokes number not previously reported. © 1997 by John Wiley & Sons, Ltd.
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  • 25
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 771-786 
    ISSN: 0271-2091
    Keywords: shallow water equations ; seiches ; stratification ; analytical solution ; validation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new analytical solution is presented for the case of a stratified seiche. This solution, especially its energetics, is useful for the validation of numerical shallow water models under stratified conditions. The utility of the analytical solution for validation is shown by using it to validate a simple finite difference numerical model. A comparison of the energetics of the numerical and analytical solutions reveals that the model results converge rapidly to the analytical solution with increasing resolution, such that a grid size of 30×30 would appear adequate for validation. In addition to properly resolving the spatial features, good temporal resolution is also necessary for validation, i.e use of a Courant number (Cr) less than one. For example, owing to the numerical dispersion of the present model, using Cr=5/4 rather than Cr =1/4 for the 50×50 grid resulted in 3·6 times larger RMS errors of model versus analytical barotropic available potential energy.This new analytical solution should be applied to a test suite of such validation tools before using such numerical models to simulate the more realistic geophysical flows encountered in lakes, bays, harbours and semi-enclosed seas under stratified conditions. © 1997 by John Wiley & Sons, Ltd.
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  • 26
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 759-769 
    ISSN: 0271-2091
    Keywords: computational fluid dynamics ; method of lines ; internal separated flows ; higher-order spatial discretization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper summarizes the method-of-lines (MOL) solution of the Navier-Stokes equations for an impulsively started incompressible laminar flow in a circular pipe with a sudden expansion. An intelligent higher-order spatial discretization scheme, which chooses upwind or downwind discretization in a zone-of-dependence manner when flow reversal occurs, was developed for separated flows. Stability characteristics of a linear advective-diffusive equation were examined to depict the necessity of such a scheme in the case of flow reversals. The proposed code was applied to predict the time development of an impulsively started flow in a pipe with a sudden expansion. Predictions were found to show the expected trends for both unsteady and steady states. This paper demonstrates the ease with which the Navier-Stokes equations can be solved in an accurate manner using sophisticated numerical algorithms for the solution of ordinary differential equations (ODEs). Solutions of the Navier-Stokes equations in primitive variables formulation by using the MOL and intelligent higher-order spatial discretization scheme are not available to date. © 1997 by John Wiley & Sons, Ltd.
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  • 27
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 893-912 
    ISSN: 0271-2091
    Keywords: numerical stability ; mixed Eulerian-Lagrangian scheme ; free surface flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A systematic methodology of numerical stability is presented here in the study of numerical properties of mixed Eulerian- Lagrangian schemes for the numerical simulation of non-linear free surface flows. Two different numerical schemes, i.e. a source-doublet panel method and a desingularized method, are investigated. The present work provides theoretical foundations and applications for numerical stability analysis theory. The matrix stability method has been developed to obtain the spectral radii and normal modes associated with free surface discretization. Some examples considered illustrate the usefulness of this analysis. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 893-912, 1997.
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  • 28
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 813-831 
    ISSN: 0271-2091
    Keywords: pre-metered ; metered ; free boundary condition ; free surface flow ; viscous ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In a forward-roll coating gap or nip, steady laminar flow of liquid between counter-rotating cylinders or rolls is used to split the flow into a coated layer on one roll and a rejected layer on the other. Both layers have free surfaces in contact with air. Liquid may be carried into the gap as a layer on one or both rolls. If the arriving layer is not too thick, all of the liquid flows through the gap, a situation called pre-metered. If the arriving layer is too thick, part of the liquid is rejected and runs back down the lower roll. The flow rate through the gap is said to be metered and is not known a priori.The transition from a pre-metered regime to the metered situation was examined by solving the Navier-Stokes system for steady, two-dimensional flow in a domain bounded by free surfaces, two rigid roll surfaces and chosen inflow and outflow surfaces. The free boundary condition, as described by Papanastasiou et al. (Int. j. numer methods fluids, 14, 587 (1992)), was explored and proved to accommodate both the pre-metered and metered regimes. A run-back flow state across the synthetic inlet plane was obtained, provided a condition on the thickness of the arriving layer was replaced by a kinematic condition at a certain stage.The coupled equation system was solved by Galerkin's method with finite element basis functions. The resulting non-linear algebraic system was solved by Newton's method with initialization by pseduo-arc-length continuation and automatic parameter step adjustment.Results show the existence of multiple solutions which can lead to hysteresis. Flow regime maps were constructed to portray the operating parameter range in which a coating bead can exist and the ranges in which a coating gap operates in either the pre-metered or the metering regime. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 813-831, 1997.
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  • 29
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 913-931 
    ISSN: 0271-2091
    Keywords: run-up ; Lagrangian co-ordinates ; finite differences ; slide-generated waves ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A Lagrangian finite difference model for non-dispersive (long) and fully non-linear surface waves is presented. The Lagrangian description enables the inclusion of run-up and back-wash at sloping shores. The numerical procedure has been verified through a series of tests, including systematic grid refinements and comparison with analytical solutions for run-up.Results for a few cases with moderately complex geometries are presented. The run-up distribution on an idealized headland is computed and discussed in view of the involved physical mechanisms. Some cases involve a time-dependent bottom topography, corresponding to a moving slide penetrating the fluid surface. The numerical solution procedure appears to be robust, unless wave breaking is encountered, and grid refinement tests show fast convergence once the scales in the problems are resolved.The presented work has been carried out under the GITEC and GITEC-TWO projects that have been funded by the European Commission, under the contracts EVCV-CT92-0175, ENV4-U96-0297, and by the Norwegian Research Council. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 913-931, 1997.
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  • 30
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 965-986 
    ISSN: 0271-2091
    Keywords: turbulence models ; k-ε ; non-linear k-ε ; finite element method ; validation ; FEAT ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Standard, modified and non-linear k-ε: turbulence models are validated against three axisymmetric flow problems - flow through a pipe expansion, flow through a pipe constriction and an impinging jet problem - to underpin knowledge about the solution quality obtained from two-equation turbulence models. The extended models improve the prediction of turbulence as a flow approaches a stagnation point and the non-linear model allows for the prediction of anisotropic turbulence. Significantly different values for the non-linear model coefficients are proposed in comparison with values found in the literature. Nevertheless, current turbulence models are still unable to accurately predict the spreading rate of shear layers. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids, 24: 965-986, 1997.
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  • 31
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1019-1035 
    ISSN: 0271-2091
    Keywords: multigrid ; supersonic flow ; turbulence ; q-ω model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A multigrid convergence acceleration technique has been developed for solving both the Navier-Stokes and turbulence transport equations. For turbulence closure a low-Reynolds-number q-ω turbulence model is employed. To enable convergence, the stiff non-linear turbulent source terms have to be treated in a special way. Further modifications to standard multigrid methods are necessary for the resolution of shock waves in supersonic flows. An implicit LU algorithm is used for numerical time integration. Several ramped duct test cases are presented to demonstrate the improvements in performance of the numerical scheme. Cases with strong shock waves and separation are included. It is shown to be very effective to treat fluid and turbulence equations with the multigrid method. A comparison with experimental data demonstrates the accuracy of the q-ω turbulence closure for the simulation of supersonic flows. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 1019-1035, 1997.
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  • 32
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1049-1072 
    ISSN: 0271-2091
    Keywords: free surface flow ; boundary element method ; Taylor series expansion ; Lagrangian derivative ; symbolic computation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the boundary element method is applied to solve transient non-linear free surface flow problems formulated from potential theory. For the temporal evolution a high-order time-stepping procedure based on a truncated forward-time Taylor series expansion is compared with the classical Runge-Kutta technique. The numerical code for both two-dimensional and axisymmetric configurations has been successfully implemented. Emphasis in the paper is placed on describing the analytical development achieved by the use of Maple software. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids, 24: 1049-1072, 1997.
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  • 33
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1091-1110 
    ISSN: 0271-2091
    Keywords: elastohydrodynamics ; fluid-membrane interactions ; moving boundary problems ; deformable spatial domain/space-time (DSD/ST) finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The interaction between the hydrodynamic forces of a flow field and the elastic forces of adjacent deformable boundaries is described by elastohydrodynamics, a coupled fluid-elastic membrane problem. Direct numerical solution of the unsteady, highly non-linear equations requires that the dynamic evolution of both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. This paper describes a numerical algorithm based on the deformable spatial domain space-time (DSD/ST) finite element method for the unsteady motion of an incompressible, viscous fluid with elastic membrane interaction. The unsteady Navier-Stoke and elastic membrane equations are solved separately using an iterative procedure by the GMRES technique with an incomplete lower-upper (ILU) decomposition at every time instant. One-dimensional, two-dimensional and deformable domain model problems are used to demonstrate the capabilities and accuracy of the present algorithm. Both steady state and transient problems are studied. © 1997 John Wiley & Sons, Ltd.
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  • 34
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 421-436 
    ISSN: 0271-2091
    Keywords: numerical analysis ; boundary conditions ; aerothermal coupling ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper analyses the numerical stability of coupling procedures in modelling the thermal diffusion in a solid and a fluid with continuity of temperature and heat flux at the interface. A simple one-dimensional model is employed with uniform material properties and grid density in each domain. A number of different explicit and implicit algorithms are considered for both the interior equations and the boundary conditions. The analysis shows that in general these are stable provided that Dirichlet boundary conditions are imposed on the fluid and Neumann boundary conditions are imposed on the solid; in each case the imposed values are obtained from the other domains. © 1997 John Wiley & Sons, Ltd.
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  • 35
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 475-491 
    ISSN: 0271-2091
    Keywords: mesh ; anisotropic ; adaptation ; Delaunay ; metric ; CFD ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Three new ideas for anisotropic adaption of unstructured triangular grids are presented, with particular emphasis on fluid flow computations. © 1997 John Wiley & Sons, Ltd.
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  • 36
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1159-1183 
    ISSN: 0271-2091
    Keywords: backward-facing step ; laminar flow ; Navier-Stokes ; finite elements ; 3D ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier-Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100≤ Re≤ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100≤Re≤ 800. © 1997 John Wiley & Sons, Ltd.
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  • 37
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1253-1270 
    ISSN: 0271-2091
    Keywords: meshless methods ; sloshing ; computational fluid dynamics ; impact ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The formulation and implementation of a three-dimensional meshless method, the element-free Galerkin (EFG) method, are described. The formulation is intended for dynamic problems with geometric and material non-linearities solved with explicit time integration, but some of the developments are applicable to other solution methods. The mechanical formulation is posed in the reference configuration so that the shape functions and their derivatives need to be computed only once. A method for speeding up the calculation of shape functions and their derivatives is presented. Results are presented for sloshing problems and Taylor bar impact problems, including an impact problem in which the bar impacts with an angle of obliquity. © 1997 John Wiley & Sons, Ltd.
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  • 38
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1291-1306 
    ISSN: 0271-2091
    Keywords: permeable sand fence ; trench trap ; three-step Taylor/Galerkin method ; k-ε turbulence model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical study of the turbulent air flow in a trench trap and the turbulent flow around a permeable sand fence is reported in this paper. The two-dimensional modified k-ε turbulence model proposed by Kato and Launder is used to predict the turbulent characteristics of the air flow. The discretization method for the governing equations is the three-step Taylor/Galerkin finite element method proposed by the authors. For the flow in a trench trap the numerical results are compared with experimental data obtained under realistic conditions using a large wind tunnel. For the air flow around a permeable sand fence a pressure loss model is used to represent the effect of the porosity of the fence on the flow field. © 1997 John Wiley & Sons, Ltd.
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  • 39
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 599-610 
    ISSN: 0271-2091
    Keywords: axisymmetric nozzles ; two-dimensional nozzles ; Navier-Stokes solver ; internal flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: MacCormack's explicit time-marching scheme is used to solve the full Navier-Stokes unsteady, compressible equations for internal flows. The requirement of a very fine grid to capture shock as well as separated flows is circumvented by employing grid clustering. The numerical scheme is applied for axisymmetric as well as two-dimensional flows. Numerical predictions are compared with experimental data and the qualitative as well as the quantitative agreement is found to be quite satisfactory. © 1997 John Wiley & Sons, Ltd.
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  • 40
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 633-644 
    ISSN: 0271-2091
    Keywords: laminar flow ; entrance effect ; backward-facing step ; sudden expansion ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The study investigates the entrance effect for flow over a backward-facing step by comparing predictions that set the inlet boundary at various locations upstream of the sudden expansion. Differences are most significant in the sudden expansion region. If the geometry has an inlet channel, then shorter reattachment and separation lengths are predicted. Comparisons with experimental data indicate that better agreement is found using a long inlet channel, but only for low Reynolds numbers where the experimental error is less significant. For certain cases, predictions with a high expansion number are perturbed by the entrance effect more than low-expansion-number predictions; however, the effect is localized in the sudden expansion region. Channels with low expansion numbers always experience a greater entrance effect after some distance upstream and downstream of the sudden expansion. The boundary layer growth in the inlet channel was examined using a uniform inlet velocity profile. © 1997 John Wiley & Sons, Ltd.
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  • 41
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 679-695 
    ISSN: 0271-2091
    Keywords: incompressible flow ; body force ; projection method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We show that a non-physical velocity may appear in the numerical computation of the flow of an incompressible fluid subjected to external forces. A distorted mesh and the use of a numerical method which does not rigorously ensure the incompressibility condition turn out to be responsible for this phenomenon. We illustrate it with numerical examples and we propose a projection method which improves the results. © 1997 John Wiley & Sons, Ltd.
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  • 42
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 719-736 
    ISSN: 0271-2091
    Keywords: finite element method ; fictitious domain method ; three-dimensional ; internal parts ; incompressible fluid flow ; constrained optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new Galerkin finite element method for the solution of the Navier-Stokes equations in enclosures containing internal parts which may be moving is presented. Dubbed the virtual finite element method, it is based upon optimization techniques and belongs to the class of fictitious domain methods. Only one volumetric mesh representing the enclosure without its internal parts needs to be generated. These are rather discretized using control points on which kinematic constraints are enforced and introduced into the mathematical formulation by means of Lagrange multipliers. Consequently, the meshing of the computational domain is much easier than with classical finite element approaches.   First, the methodology will be presented in detail. It will then be validated in the case of the two-dimensional Couette cylinder problem for which an analytical solution is available. Finally, the three-dimensional fluid flow inside a mechanically agitated vessel will be investigated. The accuracy of the numerical results will be assessed through a comparison with experimental data and results obtained with a standard finite element method. © 1997 John Wiley & Sons, Ltd.
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  • 43
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 739-748 
    ISSN: 0271-2091
    Keywords: incomplete LU preconditioning ; skyline format ; stability ; approximate inverse ; lid-driven cavity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Incomplete LU factorizations are among the most effective preconditioners for solving general large, sparse linear systems arising from practical engineering problems. This paper shows how an ILU factorization may be easily computed in sparse skyline storage format, as opposed to traditional row-by-row schemes. This organization of the factorization has many advantages, including its amenability when the original matrix is in skyline format, the ability to dynamically monitor the stability of the factorization and the fact that factorizations may be produced with symmetric structure. Numerical results are presented for Galerkin finite element matrices arising from the standard square lid-driven cavity problem. © 1997 John Wiley & Sons, Ltd.
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  • 44
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 803-823 
    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; heat transfer ; adaptive FEM ; forced convection ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents an adaptive finite element method to solve forced convective heat transfer. Solutions are obtained in primitive variables using a high-order finite element approximation on unstructured grids. Two general-purpose error estimators are developed to analyse finite element solutions and to determine the characteristics of an improved mesh which is adaptively regenerated by the advancing front method. The adaptive methodology is validated on a problem with a known analytical solution. The methodology is then applied to heat transfer predictions for two cases of practical interest. Predictions of the Nusselt number compare well with measurements and constitute an improvement over previous results. © 1997 John Wiley & Sons, Ltd.
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  • 45
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 825-845 
    ISSN: 0271-2091
    Keywords: conservation laws ; entropy inequality ; Euler equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This work deals with the relation between the numerical solutions of hyperbolic systems of conservation laws and the associated entropy evolution. An analysis of the continuum problem by means of variational calculus clearly emphasizes the consequences of the adopted reconstruction procedure on the induced entropy balance. A methodology is proposed that allows for a posterior local and global spurious entropy production estimates on the basis of an additional equation representing a discrete approximation to the entropy inequality. The problem of defining a consistent approximation of the numerical entropy flux is also addressed in detail. Properly designed numerical experiments support the analysis and contribute to providing a more comprehensive evaluation of the numerical entropy dynamics. © 1997 John Wiley & Sons, Ltd.
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  • 46
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 51-62 
    ISSN: 0271-2091
    Keywords: two-dimensional turbulence ; DNS ; vortex dynamics ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional ‘turbulent’ flow around a rectangular cylinder has been simulated at Re=10,000 using a sixth- order-accurate finite volume method for the discretization of convection and diffusion. The spatial discretization consists of a combination of a seventh- order upwind-biased method for the convective terms and an eighth-order central method for the diffusive terms, discretized on a stretched and staggered grid. To cope with the stretching of the grid, Lagrange interpolations are used.The method applied to obtain a boundary condition for the velocity in the x-direction at the outflow boundary is shown not to affect the flow in the interior of the computational domain in a way that is visible in various snapshots of the vorticity field. The variation in the velocity in the x-direction with time is itself found to be relatively small near the outflow boundary.Several turbulence statistics have been gathered from a simulation of the flow developed during 77 dimensionless time units. Snapshots of the vorticity field of the developed flow show the presence of a vortex-street- like structure. Typical 2D turbulent behaviour, such as the appearance of monopolar, dipolar and tripolar vortices due to the amalgamation of vorticity in the wake and the x-1/2 scaling of the velocity defect in the wake, has been obtained. © 1997 John Wiley & Sons, Ltd.
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  • 47
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 105-121 
    ISSN: 0271-2091
    Keywords: finite difference approximation ; planetary boundary layer problem ; spikes ; jittering ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical experiments performed with all possible combinations of approximations for the equations of a one-dimensional planetary boundary layer model employing a one-equation turbulence closure scheme and a staggered, homogeneous, finite difference grid show that spikes and jittering in the vertical profiles of predicted variables are caused by an inappropriate numerical description of the turbulent kinetic energy equation. Jittering arises when using both moderate and large time steps, while spikes occur for large time steps only. There exist two types of jittering: transient and permanent. The former has a lifetime of about 1 week and occurs with large time steps. Permanent jittering, on the other hand, is observed when using moderate time steps and has a lifetime of more than a 1000 days. Introducing an iterative procedure for the eddy viscosity eliminates spikes and permanent jittering but is unsuccessful in removing transient jittering. It is further found that the transition to instability of the solution can be either a sudden or a gradual one. In the case of a sudden transition no numerical peculiarities are observed, whereas for a gradual transition to instability, jittering is present during the entire transition period. In this sense, jittering may be regarded as a herald of instability. Finally, a combination which employs implicit approximations consistently for all the terms in the model equations, regardless of whether using an implicit or semi-implicit approximation for the Coriolis term, proves to be devoid of any numerical artefacts without the need for introducing the iterative procedure for the eddy viscosity. © 1997 John Wiley & Sons, Ltd.
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  • 48
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 125-142 
    ISSN: 0271-2091
    Keywords: viscous ; vorticity ; detached separation ; cylinder ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The origination of detached separation is studied on the basis of a numerical solution of the full Navier-Stokes equations. Fluxes of vorticity with different signs generated with twice the frequency of cylinder oscillation move from the cylinder to the outer surface of a detached liquid layer in the form of concentric rings. Near the critical layer between the attached layer and the main flow these rings are torn and crimped to the regions of separated vortices of the corresponding sign. The form of detached separated vortices is similar to that of vortices originating from a stationary circular cylinder in a uniform flow. Transition of the flow to a non-symmetric form with Karman vortex street generation at a Reynolds number (based on the radius) greater than 17 is revealed. This critical Reynolds number is smaller than that for a stationary circular cylinder in a viscous stream (where Re=20 has been determined to be a critical value) and corresponds to the Reynolds number extrapolated from the critical value for the stationary cylinder by increasing the cylinder radius by the attached layer thickness. The vorticity flux from the cylinder surface immediately into the separation region decreases as the frequency of cylinder oscillation increases. Violation of the flow potentiality in the detached separation region is the main cause of the vorticity generation on the outer surface of the attached liquid layer. © 1997 John Wiley & Sons, Ltd.
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  • 49
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 183-203 
    ISSN: 0271-2091
    Keywords: shape design ; turbulent flow ; automatic differentiation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new approach for optimal shape design is introduced. The main ingredients are an unstructured CAD-free framework for geometry deformation and automatic differentiation (AD) in reverse mode. Transonic inviscid and viscous turbulent flows are investigated. Both two- and three- dimensional configurations are considered. These cases involve up to several thousand control parameters. © 1997 John Wiley & Sons, Ltd.
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  • 50
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 205-223 
    ISSN: 0271-2091
    Keywords: optimal control ; Navier-Stokes equations ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We study the numerical solution of optimal control problems associated with two-dimensional viscous incompressible thermally convective flows. Although the techniques apply to more general settings, the presentation is confined to the objectives of minimizing the vorticity in the steady state case and tracking the velocity field in the non-stationary case with boundary temperature controls. In the steady state case we develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed; finite element methods are used to find approximate solutions for the optimality system of equations. In the time-dependent case a piecewise-in-time optimal control approach is proposed and the fully discrete approximation algorithm for solving the piecewise optimal control problem is defined. Numerical results are presented for both the steady state and time-dependent optimal control problems. © 1997 John Wiley & Sons, Ltd.
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  • 51
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 249-263 
    ISSN: 0271-2091
    Keywords: lattice Boltzmann ; boundary conditions ; bounce-back; accuracy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltemann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0·1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder. The bounce-back boundary condition is shown to yield accurate lattice Boltzmann simulations with reduced computational requirements for computational grids of 170×170 or finer, a relaxation time less than 1·5 and any Reynolds number from 0·1 to 100. For this range of parameters the root mean square error in velocity and the relative error in drag coefficient are less than 1 per cent for the octagonal cylinder and 2 per cent for the circular cylinder. © 1997 John Wiley & Sons, Ltd.
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  • 52
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 265-283 
    ISSN: 0271-2091
    Keywords: open boundary conditions ; Poiseuille-Bénard flow ; augmented Lagrangian ; thermal instabilities ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The main objective of this study is to compare the influence of different boundary conditions upon the incompressible Poiseuille -Bénard channel flow (PBCF) in a 2D rectangular duct heated from below. In a first technical part the algorithm used to carry out this work, based on the augmented Lagrangian method, is presented. The implementation details of the five different open boundary conditions (OBCs) and the periodic boundary conditions (PBCs) tested in the present paper are also given. The study is then carried out for 1800〈Ra≤ 10,000, 0〈Re≤10 and 0·67≤Pr≤6·4. The five selected OBCs, applied at the outlet of the computational domain, respectively express the following conditions: a square profile for the velocity (OBC1), mass conservation (OBC2), zero second derivative of the horizontal velocity component (OBC3), a mixed boundary condition combining Dirichlet and Neumann conditions (OBC4) and an Orlanski-type boundary condition (OBC5). A good estimation of the perturbation amplitude and of the length of the perturbed zone at the outlet boundary is proposed. It is shown that OBC5 causes very little perturbation in the recirculating flow compared with the other OBCs. © 1997 John Wiley & Sons, Ltd.
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  • 53
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 285-313 
    ISSN: 0271-2091
    Keywords: shallow-water ; soluteep ; solver ; turbulence ; model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A 3D semi-implicit finite volume scheme for shallow- water flow with the hydrostatic pressure assumption has been developed using the σ-co-ordinate system, incorporating a standard k-ε turbulence transport model and variable density solute transport with the Boussinesq approximation for the resulting horizontal pressure gradients. The mesh spacing in the vertical direction varies parabolically to give fine resolution near the bed and free surface to resolve high gradients of velocity, k and ε. In this study, wall functions are used at the bed (defined by the bed roughness) and wind stress at the surface is not considered. Surface elevation gradient terms and vertical diffusion terms are handled implicitly and horizontal diffusion and source terms explicitly, including the Boussinesq pressure gradient term due to the horizontal density gradient. The advection terms are handled in explicit (conservative) form using linear upwind interpolation giving second-order accuracy. A fully coupled solution for the flow field is obtained by substi- tuting for velocity in the depth-integrated continuity equation and solving for surface elevation using a conjugate gradient equation solver. Evaluation of horizontal gradients in the σ-co-ordinate system requires high-order derivatives which can cause spurious flows and this is avoided by obtaining these gradients in real space. In this paper the method is applied to parallel oscillatory (tidal) flow in deep and shallow water and compared with field measurements. It is then applied to current flow about a conical island of small side slope where vortex shedding occurs and velocities are compared with data from the laboratory. Computed concentration distributions are also compared with dye visualization and an example of the influence of temperature on plume dispersion is presented. © 1997 John Wiley & Sons, Ltd.
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  • 54
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 371-392 
    ISSN: 0271-2091
    Keywords: adaptive grids ; finite element method ; iterative solvers ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the development of the three- dimensional prolonged adaptive finite element equation solver for the Navier-Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An element in the grid is refined when the Reynolds number of the element exceeds a preset limit. The global Reynolds number in the investigation is increased by scaling the solution for a lower Reynolds number. The grid is refined according to the scaled solution and the prolonged solution for the lower Reynolds number constitutes the start vector for the higher Reynolds number. Since the Reynolds number is the ratio of convection to diffusion, the grid refinements act as linearization and symmetrization of the equation system. The linear equation system of the Newton formulation is solved by CGSTAB with coupled node fill-in preconditioner. The test problem considered is the three-dimensional driven cavity flow. © 1997 John Wiley & Sons, Ltd.
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  • 55
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 407-420 
    ISSN: 0271-2091
    Keywords: wave ; finite element ; deforming mesh ; run-up ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The finite element method is developed to solve the problem of wave run-up on a mild, plane slope. A novel approach to implementing a deforming mesh of one-dimensional, three-node, isoparametric elements is described and demonstrated. The discrete time interval (DTI), arbitrary Lagrangian-Eulerian (ALE) and space-time element (STE) methods are used to solve the unsteady one-dimensional shallow water wave equations. The boundary condition required is simply the seaward water surface elevation, and although the method has only been tested for monochromatic waves, it should be equally valid for any sea state which can be described as a water surface elevation as a function of time. All three solution methods are shown to given good results. Time histories of the terms of the governing equations are calculated and used to demonstrate how the ALE and STE methods account for mesh deformation. The model could be extended to two dimensions, which would have practical application to the run-up of obliquely incident waves. © 1997 John Wiley & Sons, Ltd.
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  • 56
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 437-454 
    ISSN: 0271-2091
    Keywords: Green element method ; diffusion-advection ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: New discrete element equations or coefficients are derived for the transient 1D diffusion-advection or transport equation based on the Green element replication of the differential equation using linear elements. The Green element method (GEM), which solves the singular boundary integral theory (a Fredholm integral equation of the second kind) on a typical element, gives rise to a banded global coefficient matrix which is amenable to efficient matrix solvers. It is herein derived for the transient 1D transport equation with uniform and non-uniform ambient flow conditions and in which first-order decay of the containment is allowed to take place. Because the GEM implements the singular boundary integral theory within each element at a time, the integrations are carried out in exact fashion, thereby making the application of the boundary integral theory more utilitarian. This system of discrete equations, presented herein for the first time, using linear interpolating functions in the spatial dimensions shows promising stable characteristics for advection-dominant transport. Three numerical examples are used to demonstrate the capabilities of the method. The second-order-correct Crank-Nicolson scheme and the modified fully implicit scheme with a difference weighting value of two give superior solutions in all simulated examples. © 1997 John Wiley & Sons, Ltd.
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  • 57
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 495-512 
    ISSN: 0271-2091
    Keywords: separated flows ; recirculation length ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The incompressible, laminar, isothermal flow of a Newtonian fluid at steady state past a surface-mounted obstacle (flow over a step) is studied in a two-dimensional numerical experiment using the Galerkin finite element method. The dimensionless Navier-Stokes equations are solved in the whole range of the laminar flow regime. The numerical predictions are compared with available experimental data. The emphasis in the discussion of the results is on the presentation of the streamlines for various Reynolds numbers, the pressure distribution over and downstream of the step, the shear stress distribution along the surface of the step and the length of the recirculation region as a function of the Reynolds number. This analysis may be used in numerous applications from agricultural to civil, mechanical and chemical engineering. © 1997 John Wiley & Sons, Ltd.
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  • 58
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 567-598 
    ISSN: 0271-2091
    Keywords: free surface flows ; finite volumes ; k-ε model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Systematic tests have been performed to study the behaviour of a numerical method developed to calculate 2D, steady free surface flows. The Reynolds equations are solved in the physical space by employing a non-orthogonal staggered grid, while the k-ε model is adopted to approximate the Reynolds stresses. The free surface is calculated following an iterative procedure and various parameters that affect convergence and accuracy of the numerical solution have been examined. Calculated results are compared with measured data for two cases, i.e. the wave generation above a bottom topography at various Froude numbers and the free surface formation above a submerged hydrofoil. © 1997 John Wiley & Sons, Ltd.
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  • 59
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 523-545 
    ISSN: 0271-2091
    Keywords: incompressible Navier-Stokes equations ; flux-vector-splitting method ; artificial compressibility ; upwind schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An implicit, upwind arithmetic scheme that is efficient for the solution of laminar, steady, incompressible, two-dimensional flow fields in a generalised co-ordinate system is presented in this paper. The developed algorithm is based on the extended flux-vector-splitting (FVS) method for solving incompressible flow fields. As in the case of compressible flows, the FVS method consists of the decomposition of the convective fluxes into positive and negative parts that transmit information from the upstream and downstream flow field respectively. The extension of this method to the solution of incompressible flows is achieved by the method of artificial compressibility, whereby an artificial time derivative of the pressure is added to the continuity equation. In this way the incompressible equations take on a hyperbolic character with pseudopressure waves propagating with finite speed. In such problems the ‘information’ inside the field is transmitted along its characteristic curves. In this sense, we can use upwind schemes to represent the finite volume scheme of the problem's governing equations. For the representation of the problem variables at the cell faces, upwind schemes up to third order of accuracy are used, while for the development of a time-iterative procedure a first-order-accurate Euler backward-time difference scheme is used and a second-order central differencing for the shear stresses is presented. The discretized Navier-Stokes equations are solved by an implicit unfactored method using Newton iterations and Gauss-Siedel relaxation. To validate the derived arithmetical results against experimental data and other numerical solutions, various laminar flows with known behaviour from the literature are examined. © 1997 John Wiley & Sons, Ltd.
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  • 60
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 233-245 
    ISSN: 0271-2091
    Keywords: observers ; gas pipelines ; optimal control ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Seeking the optimal operating policy by an off-line controller for pipelines carrying natural gas has an inherent state estimation problem associated with deviations from demand forecast. This paper presents a Kalman-filter-based observer for the real-time estimation of deviations from the states previously obtained by an off-line controller optimally, around an expected demand function. The observer is based on the linearized form of the non-linear partial differential equations which are the state space representation of isothermal and unidirectional gas flow through a pipeline. Data for the observer are produced by a dynamic simulator. The simulator and linearized observer equations are solved using an implicit finite element method. The observer has been tested on a pipeline subject to certain deviations from demand forecast. It converge s in a short span of time. © 1997 by John Wiley & Sons, Ltd.
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  • 61
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 253-274 
    ISSN: 0271-2091
    Keywords: bluff body ; hybrid vortex method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A hybrid vortex method was developed to simulate the two-dimensional viscous incompressible flows over a bluff body numerically. It is based on a combination of the diffusion-vortex method and the vortex-in-cell method by dividing the flow field into two regions. In the region near the body surface the diffusion-vortex method is used to solve the Navier-Stokes equations, while the vortex-in-cell method is used in the exterior domain. Comparison with results obtained by the finite difference method, other vortex methods and experiments shows that the present method is well adapted to calculate two-dimensional external flows at high Reynolds number. It is capable of calculating not only the global characteristics of the separated flow but also the evolution of the fine structure of the flow field with time precisely. The influence of the grid system and region decomposition on the results will also be discussed. © by 1997 John Wiley & Sons, Ltd.
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  • 62
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 275-290 
    ISSN: 0271-2091
    Keywords: pulsatile flow ; ring-type constrictions ; numerical experimentation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The effects of pulsatile amplitude on sinusoidal laminar flows through a rigid pipe with sharp-edged ring-type constrictions have been studied numerically. The parameters considered are: mean Reynolds number (Re) of the order of 100; Strouhal number (St) in the range 0·0-3·98; Womersley number (Nw) in the range 0·0-50·0. The pulsatile amplitude (A) varies in the range 0·0-2·0. The flow characteristics were studied through the pulsatile contours of streamline, vorticity, shear stress and isobars. Within a pulsatile cycle the relations between instantaneous flow rate (Q) and instantaneous pressure gradient (dp/dz) are observed to be elliptic. The relations between instantaneous flow rate (Q) and pressure loss (Ploss) are quadratic. Linear relations exist between instantaneous flow rate (Q) and maximum velocity, maximum vorticity and maximum shear stress. © by 1997 John Wiley & Sons, Ltd.
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  • 63
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 875-892 
    ISSN: 0271-2091
    Keywords: adaptive parallel multigrid method ; local refinement criteria ; incompressible Navier-Stokes equations ; hole pressure problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper an adaptive parallel multigrid method and an application example for the 2D incompressible Navier-Stokes equations are described. The strategy of the adaptivity in the sense of local grid refinement in the multigrid context is the multilevel adaptive technique (MLAT) suggested by Brandt. The parallelization of this method on scalable parallel systems is based on the portable communication library CLIC and the message-passing standards: PARMACS, PVM and MPI. The specific problem considered in this work is a two-dimensional hole pressure problem in which a Poiseuille channel flow is disturbed by a cavity on one side of the channel. Near geometric singularities a very fine grid is needed for obtaining an accurate solution of the pressure value. Two important issues of the efficiency of adaptive parallel multigrid algorithms, namely the data redistribution strategy and the refinement criterion, are discussed here. For approximate dynamic load balancing, new data in the adaptive steps are redistributed into distributed memories in different processors of the parallel system by block remapping. Among several refinement criteria tested in this work, the most suitable one for the specific problem is that based on finite-element residuals from the point of view of self-adaptivity and computational efficiency, since it is a kind of error indicator and can stop refinement algorithms in a natural way for a given tolerance. Comparisons between different global grids without and with local refinement have shown the advantages of the self-adaptive technique, as this can save computer memory and speed up the computing time several times without impairing the numerical accuracy. © 1997 By John Wiley & Sons, Ltd. Int. J. Numer. Methods Fluids 24, 875-892, 1997.
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  • 64
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 319-336 
    ISSN: 0271-2091
    Keywords: coupling ; film condensation ; natural convection ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Theoretical analyses which incorporate one-dimensional heat conduction along a plate and transverse heat conduction approximations are presented to predict the net heat transfer between laminar film condensation of a saturated vapour on one side of a vertical plate and boundary layer natural convection on the other side. It is assumed that countercurrent boundary layer flows are formed on the two sides. The governing boundary layer equations of this problem and their corresponding boundary conditions are all cast into dimensionless forms by using a non-similarity transformation. Thus the resulting system of equations can be solved by using the local non-similarity method for the boundary layer equations and a finite difference method for the heat conduction equation of the plate. The plate temperature and the heat flux through the plate are repetitively determined until the solutions for each side of the plate match. The predicted results show that the effect of Prc is not negligible for larger values of A* (thermal resistance ratio between natural convecti on side and condensing film side) and the approximation of transverse heat conduction overpredicts the plate temperature for lower values of Rt (thermal resistance ratio between plate and condensing film). However, no significant differences are observed between the two different approximations for higher values of Rt. © by 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 939-951 
    ISSN: 0271-2091
    Keywords: vortex filament method ; parallel machines ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper addressed the implementation of vortex filament methods on parallel machines with distributed memory to simulate a three-dimensionally evolving jet. Vortical structure developments due to Kelvin-Helmholtz instability of the axially perturbed jet are also examined. The implementation is conducted in a single-programme multiple-data (SPMD) environment and the parallelism is focused on issues of data distribution, efficient support of parallel I/O and overlapping of communications with computations. In addition, since the number of segment markers in a filament is dynamically growing according to the requirement of numerical accuracy, a novel packet-oriented data structure is proposed not only to partition filament segment markers among distributed processors but also to support dynamical load balancing at run time. This work is the first to apply packet-oriented structures to implement a parallel vortex filament method. Experimental results indicate performance improvement from 1·5 to 2·6 times over static schemes on nCUBE2, DEC Alpha and IBM SP2 by incorporating the proposed scheme with packet-oriented structures. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 939-951, 1997.
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  • 66
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 953-963 
    ISSN: 0271-2091
    Keywords: coastal hydrodynamics ; shallow water equations ; finite element method ; finite difference method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the results of some studies on the development and application of a finite element method (FEM) with a closed-form solution technique for time discretization. The closed-form solution is based on the eigenvalues/vectors of a coefficient matrix. The method is first applied to the one-dimensional linearized shallow water equations and then extended to the two-dimensional shallow water equations. An attempt is made to improve its efficiency by incorporating time splitting and using the closed-form solution technique only for linear terms. Some case studies of a rectangular channel and harbour are presented to illustrate the satisfactory working of the method. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 953-963, 1997.
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  • 67
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 987-1017 
    ISSN: 0271-2091
    Keywords: pressure gradient force ; steep topography ; terrain-following coordinates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The error in computing the horizontal pressure gradient force near steep topography is investigated in a primitive equation, σ-co-ordinate, numerical ocean model (Blumberg and Mellor, in Three -Dimensional Coastal Ocean Models, Vol. 4, American Geophysical Union, Washington D.C., 1987, pp. 1-16). By performing simple test experiments where the density field is allowed to vary in both the vertical and the horizontal direction, severe errors are detected in the areas where the isopycnals hit the sloping bottom. An alternative method of computing the pressure force (Stelling and van Kester), Int. j. numer. methods fluids, 18, 915-935 (1994) is adopted, resulting in substantial reduction of the errors. However, a systematic underestimation of the calculated quantities is revealed, leading to erroneous depth-mean values of the pressure force. In this study a modification of the Stelling and van Kester method is proposed which seems to improve the overall performance of the method. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 987-1017, 1997.
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  • 68
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 393-411 
    ISSN: 0271-2091
    Keywords: advection-diffusion ; outflow boundary conditions ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We use a one-dimensional model problem of advection- diffusion to investigate the treatment recently advocated by Papanastasiou and colleagues to deal with boundary conditions at artificial outflow boundaries.Using finite elements of degree p, we show that their treatment is equivalent to imposing the condition that the (p+1 )st derivative of the dependent variable should vanish at a point close to the outflow. This is then shown to lead to errors of order O((h+1/Pe)1.6p+1) in the numerical solutions (where h is the maximum element size and Pe is the global Peclet number), which is superior to the errors of order O(hp+1+1/Pe) obtained using a standard no-flux outflow condition. These findings are verified by numerical experiments. © 1997 by John Wiley and Sons, Ltd.
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  • 69
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 413-417 
    ISSN: 0271-2091
    Keywords: open boundaries ; extrapolation conditions ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In recent work on outflow boundary conditions for Navier-Stokes equations by Papanastasiou et al. (Int. j. numer. methods fluids, 14, 587-608 (1992)) a choice has been proposed which can formally be described as imposing no boundary condition at all. This of course leads to an underdetermined problem at the level of the partial differential equations. However, it yields a well-defined problem at the discrete level and it has been documented that this choice of outflow conditions performs in a way which is superior to more ‘standard’ artificial boundary conditions. In this paper we analyse a one-dimensional model problem. We shall show that the ‘free’ boundary condition of Papanastasiou et al. actually imposes an effective boundary condition. This effective boundary condition is identified and its advantages are discussed. © 1997 by John Wiley and Sons, Ltd.
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  • 70
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 477-492 
    ISSN: 0271-2091
    Keywords: finite element ; continuation ; Hopf bifurcation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present results of a stability analysis of the lid-driven cavity flow based on classical C0 finite element discretizations of the Navier-Stokes system. Using arc length continuation and subspace iteration to compute the eigenvalues of the tangent operator, we study the dependence of the bifurcation diagram and of the spectrum on the chosen discretization. © 1997 by John Wiley & Sons, Ltd.
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  • 71
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 423-439 
    ISSN: 0271-2091
    Keywords: transport equation ; wave equation model ; FEM ; mass lumping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The wave equation model, originally developed to solve the advection-diffusion equation, is extended to the multidimensional transport equation in which the advection velocities vary in space and time. The size of the advection term with respect to the diffusion term is arbitrary. An operator-splitting method is adopted to solve the transport equation. The advection and diffusion equations are solved separate ly at each time step. During the advection phase the advection equation is solved using the wave equation model. Consistency of the first-order advection equation and the second-order wave equation is established. A finite element method with mass lumping is employed to calculate the three-dimensional advection of both a Gaussian cylinder and sphere in both translational and rotational flow fields. The numerical solutions are accurate in comparison with the exact solutions. The numerical results indicate that (i) the wave equation model introduces minimal numerical oscillation, (ii) mass lumping reduces the computational costs and does not significantly degrade the numerical solutions and (iii) the solution accuracy is relatively independent of the Courant number provided that a stability constraint is satisfied. © 1997 by John Wiley & Sons, Ltd.
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  • 72
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 457-476 
    ISSN: 0271-2091
    Keywords: transonic full potential equation ; Newton iteration ; preconditioned conjugate gradient ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper, numerical methods for solving the transonic full potential equation are developed. The governing equation is discretized by a flux-biasing finite volume method. The resulting non-linear algebraic system is solved by using a continuation method with full Newton iteration. The continuation method is based on solving a highly ‘upstream-weighted’ discretization and then gradually reducing the upstream weighting. A general PCG-like sparse matrix iterative solver is used to solve the Jacobians at each non-linear step. Various types of incomplete LU (ILU) preconditioners and ordering techniques are compared. Numerical results are presented to demonstrate that these methods are efficient and robust for solving the transonic potential equation in the workstation computing environment. © 1997 by John Wiley & Sons, Ltd.
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  • 73
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1433-1448 
    ISSN: 0271-2091
    Keywords: flow simulation ; moving mechanical components ; fluid-structure interactions ; two-fluid interfaces ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The application of a stabilized space-time finite element formulation to problems involving fluid-structure interactions and two-fluid interfaces is discussed. Two sample problems are presented and the method is validated by comparison with a test problem. © 1997 John Wiley & Sons, Ltd.
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  • 74
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 1-19 
    ISSN: 0271-2091
    Keywords: boundary elements ; viscous flow ; gravity currents ; Stokes ; creeping ; spreading ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The viscous gravity spreading of a blob of fluid on a rigid, horizontal, no-slip surface is studied numerically by applying the boundary-element method to the Stokes equation in plane symmetry. The two-dimensional unsteady solution is obtained by solving the biharmonic equation for the streamfunction in a given domain to obtain the velocity field, which is then used to track the contour. The spreading is developed by letting adhere to the rigid boundary any fluid element set in contact with it. A detailed description of the two-dimensional flow near the head of a viscous gravity current shows a typical rolling motion which characterizes the advancing mechanism of the spreading. In particular, we obtain scaling laws for the shape and size of the current head in good agreement with previously reported experimental data. Attention is also paid to the validation of the numerical method. © 1997 by John Wiley & Sons, Ltd.
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  • 75
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 81-104 
    ISSN: 0271-2091
    Keywords: 3D tetrahedral adaptation ; time-dependent ; shock capturing ; shock diffraction ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we present a tetrahedron-based, h-refinement-type algorithm for the solution of problems in 3D gas dynamics using unstructured mesh adaptation. The mesh adaptation algorithm is coupled to a cell-centred, Riemann problem-based, finite volume scheme of the MUSCL type, employing an approximate Riemann solver. The adaptive scheme is then used to compute the diffraction of shock waves around a box section corner for subsonic and supersonic post-shock flow. In the subsonic case, preliminary measurements of vortex filament speed and vortical Mach number are in broad quantitative agreement with known theoretical results. © 1997 John Wiley & Sons, Ltd.
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  • 76
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 63-80 
    ISSN: 0271-2091
    Keywords: turbulent flows ; compressible flows ; pressure correction ; approximate factorization ; density biasing ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The steady state Navier-Stokes equations are solved in transonic flows using an elliptic formulation. A segregated solution algorithm is established in which the pressure correction equation is utilized to enforce the divergence-free mass flux constraint. The momentum equations are solved in terms of the primitive variables, while the pressure correction field is used to update both the convecting mass flux components and the pressure itself. The velocity components are deduced from the corrected mass fluxes on the basis of an upwind-biased density, which is a mechanism capable of overcoming the ellipticity of the system of equations, in the transonic flow regime. An incomplete LU decomposition is used for the solution of the transport-type equations and a globally minimized residual method resolves the pressure correction equation. Turbulence is resolved through the k-ε model. Dealing with turbomachinery applications, results are presented in two-dimensional compressor and turbine cascades under design and off-design conditions. © 1997 John Wiley & Sons, Ltd.
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  • 77
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 143-149 
    ISSN: 0271-2091
    Keywords: transient compressible flow ; finite element ; quadrature ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite volume-element formulation of the Navier-Stokes equations for compressible flows is applied to the transient shock tube problem. A second-order spatial quadrature for volumetric integration is studied because of its effects on the shock wave resolution and positioning. Low quadrature order is shown to produce solution anomalies in regions with a transonic character as well as poor predictions of shock wave propagation. The second-order volumetric quadrature includes the proper upstream and downstream solution behaviour and eliminates both the transonic and shock speed errors in the transient shock tube problem. © 1997 John Wiley & Sons, Ltd.
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  • 78
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 315-366 
    ISSN: 0271-2091
    Keywords: viscous flow ; dynamic stall ; turbulent flow ; aerofoils ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The so-called CPI finite volume method is applied to the computation of the deep dynamic stall of a pitching NACA 0012 aerofoil. The evolution of flow sequences is analysed for two turbulence models, the so-called Baldwin-Barth and K-ω SST models, and compared with available data of McAlister et al. The hysteresis loops for the force coefficients are presented for three different reduced frequencies of the pitching motion and compared with experimental data. The agreement with available data is good during the upstroke phase and it is found that the level of disagreement during the downstroke phase can be attributed to the overestimation of the pressure minima within shed vortices. © 1997 John Wiley & Sons, Ltd.
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  • 79
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 155-168 
    ISSN: 0271-2091
    Keywords: tri-tree multigrid ; ILU coupled node fill-in preconditioner ; element Reynolds number ; adaptive refinements ; adaptive recoarsements ; grid iterations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The tri-tree algorithm for refinements and recoarsements of finite element grids is explored. The refinement-recoarsement algorithm not only provides an accurate solution in certain parts of the grid but also has a major influence on the finite element equation system itself. The refinements of the grid lead to a more symmetric and linear equation matrix. The recoarsements will ensure that the grid is not finer than is necessary for preventing divergence in an iterative solution procedure. The refinement-recoarsement algorithm is a dynamic procedure and the grid is adapted to the instant solution.In the tri-tree multigrid algorithm the solution from a coarser grid is scaled relatively to the increase in velocity boundary condition for the finer grid. In order to have a good start vector for the solution of the finer grid, the global Reynolds number or velocity boundary condition should not be subject to large changes. For each grid and velocity solution the element Reynolds number is computed and used as the grid adaption indicator during the refinement-recoarsement procedure.The iterative tri-tree multigrid method includes iterations with respect to the grid. At each Reynolds number the same boundary condition s are applied and the grid is adapted to the solution iteratively until the number of unknowns and elements in the grid becomes constant. In the present paper the following properties of the tri-tree algorithm are explored: the influence of the increase in boundary velocities and the size of the grid adaption indicator on the amount of work for solving the equations, the number of linear iterations and the solution error estimate between grid levels. The present work indicates that in addition to the linear and non-linear iterations, attention should also be given to grid adaption iterations. © 1997 by John Wiley & Sons, Ltd.
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  • 80
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 185-214 
    ISSN: 0271-2091
    Keywords: viscous free surface flows ; approximate factorization ; multigrid technique ; water sloshing ; experimental validation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A modified MAC method (SIMAC; semi-implicit marker and cell) is proposed which accurately treats unsteady high-Reynolds free surface problems. SIMAC solves the Navier-Stokes equations in primitive variables on a non-uniform staggered Cartesian grid by means of a finite difference scheme. The convective term is treated explicitly by employing a second-order upwind scheme in space (HLPA) and the Adams-Bashforth technique in time. The diffusive part is solved by means of the implicit approximate factorization technique. A multigrid technique based on the additive correction strategy is employed to solve the Poisson equation for the pressure. Finally, the free surface treatment is carried out using massless particles which divide the domain of integration into full and empty cells as in a standard MAC method.The algorithm is used for the analysis of large-amplitude water sloshing in rectangular unbaffled and baffled containers. Experimental tests have been carried out in order to validate the algorithm. Numerical results satisfactorily agree with experimental data for the whole range of filing conditions analysed here. © 1997 by John Wiley & Sons, Ltd.
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  • 81
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 291-317 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; dense gas dispersion ; density stratification ; anisotropic turbulent viscosity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A state-of-the-art model is developed for the simulation of the dispersion of hazardous toxic or flammable gases heavier than air in the atmosphere. The model depends on solving the Reynolds-averaged Navier-Stokes equations in addition to the energy equation and a species concentration equation for the contaminant gas. Turbulence closure is achieved by using a buoyancy-extended version of the standard k- ∊ two-equation model. The buoyancy extension is introduced to account for the anisotropic turbulent viscosity resulting from the strong stratification introduced by the dense gas clouds. The spatial discretization is achieved via the Galerkin finite element method, while the solution is advanced in time using the forward Euler method. A special element layer is introduced in the near-ground region to bridge the gap between the solid wall and the main solution domain where the turbulence model can be applied. This special element layer eliminates the need to apply the wall function in the standard way where any oscillations in the pressure field could contaminate the velocity solution. The model was tested against the Burro-8 field trial and could predict the experiment satisfactorily to within the experimental uncertainties of the reported results. © by 1997 John Wiley & Sons, Ltd.
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  • 82
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 833-861 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; incompressible ; unsteady ; finite difference ; finite element ; non-staggered grid ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A hybrid conservative finite difference/finite element scheme is proposed for the solution of the unsteady incompressible Navier-Stokes equations. Using velocity-pressure variables on a non-staggeredgrid system, the solution is obtained with a projection method basedon the resolution of a pressure Poisson equation.The new proposed scheme is derived from the finite element spatial discretization using the Galerkin method with piecewise bilinear polynomial basis functions defined on quadrilateral elements. It is applied to the pressure gradient term and to the non-linear convection term as in the so-called group finite element method. It ensures strong coupling between spatial directions, inhibiting the development of oscillations during long-term computations, as demonstrated by the validation studies.Two- and three-dimensional unsteady separated flows with open boundaries have been simulated with the proposed method using Cartesian uniform mesh grids. Several examples of calculations on the backward-facing step configuration are reported and the results obtained are compared with those given by other methods. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 833-861, 1997.
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  • 83
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 355-373 
    ISSN: 0271-2091
    Keywords: computational fluid dynamics ; transonic airfoils ; numerical uncertainty ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical uncertainties are quantified for calculations of transonic flow around a divergent trailing edge (DTE) supercritical aerofoil. The Reynolds-averaged Navier-Stokes equations are solved using a linearized block implicit solution procedure and mixing-length turbulence model. This procedure has reproduced measurements around supercritical aerofoils with blunt trailing edges that have shock, boundary layer and separated regions. The present effort quantifies numerical uncertainty in these calculations using grid convergence indices which are calculated from aerodynamic coefficients, shock location, dimensions of the recirculating region in the wake of the blunt trailing edge and distributions of surface pressure coefficients. The grid convergence index is almost uniform around the aerofoil, except in the shock region and at the point where turbulence transition was fixed. The grid convergence index indicates good convergence for lift but only fair convergence for moment and drag and also confirms that drag calculations are more sensitive to numerical error. © 1997 by John Wiley and Sons, Ltd.
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  • 84
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 375-392 
    ISSN: 0271-2091
    Keywords: adaptive mesh refinement ; error estimation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A methodology for local solution-adaptive mesh refinement in computational fluid dynamics (CFD) using cell-level and global kinetic energy balances is formulated and tested. Results are presented for two two-dimensional steady incompressible laminar benchmark problems: a lid-driven cavity (Reynolds number Re=1000) and a backward-facing step (Re=400). It is demonstrated that local kinetic energy imbalance correlates with local solution accuracy, that normalized global imbalance is an appropriate criterion for halting mesh refinement and that a specified level of accuracy is realized at lower computational effort using local refinement compared with a uniform finer mesh. © 1997 by John Wiley and Sons, Ltd.
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  • 85
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1037-1047 
    ISSN: 0271-2091
    Keywords: tri-tree full multigrid ; ILU coupled node fill-in preconditioner ; element Reynolds number ; adaptive refinements ; adaptive recoarsement ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The full adaptive multigrid method is based on the tri-tree grid generator. The solution of the Navier-Stokes equations is first found for a low Reynolds number. The velocity boundary conditions are then increased and the grid is adapted to the scaled solution. The scaled solution is then used as a start vector for the multigrid iterations. During the multigrid iterations the grid is first recoarsed a specified number of grid levels. The solution of the Navier-Stokes equations with the multigrid residual as right-hand side is smoothed in a fixed number of Newton iterations. The linear equation system in the Newton algorithm is solved iteratively by CGSTAB preconditioned by ILU factorization with coupled node fill-in. The full adaptive multigrid algorithm is demonstr ated for cavity flow. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 1037ndash;1047, 1997.
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  • 86
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1079-1090 
    ISSN: 0271-2091
    Keywords: wake flow ; free surface ; instability ; GDQ method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The instability character of a wake in the presence of a free surface is examined by a recently developed GDQ (generalized differential quadrature) numerical method. It is shown that at low Froude number the wake near a free surface is convectively unstable, but when the Froude number is increased further it becomes absolutely unstable. The effect of water depth on the stability property of the wake flow is also investigated. It is found that the influence of water depth on the critical point of instability is limited to at most 20% variation in the complex frequency, while the change in temporal growth rate is also limited to about 20%. © 1997 John Wiley & Sons, Ltd.
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  • 87
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1111-1128 
    ISSN: 0271-2091
    Keywords: pressure correction ; block-implicit ; finite volume ; parallel ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A comparison of a new parallel block-implicit method and the parallel pressure correction procedure for the solution of the incompressible Navier-Stokes equations is presented. The block-implicit algorithm is based on a pressure equation. The system of non-linear equation s is solved by Newton's method. For the solution of the linear algebraic systems the Bi-CGSTAB algorithm with incomplete lower-upper (ILU) decomposition of the matrix is applied. Domain decomposition serves as a strategy for the parallelization of the algorithms. Different algorithms for the parallel solution of the linear system of algebraic equations in conjunction with the pressure correction procedure are proposed. Three different flows are predicted with the parallel algorithms. Results and efficiency data of the block-implicit method are compared with the parallel version of the pressure correction algorithm. The block-implicit method is characterized by stable convergence behaviour, high numerical efficiency, insensitivity to relaxation parameters and high spatial accuracy. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 18 Ill.
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  • 88
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1185-1210 
    ISSN: 0271-2091
    Keywords: Hopf bifurcation ; hydrodynamic stability ; Navier-Stokes equations ; eigenproblem ; direct simulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the precise localization of Hopf bifurcations in various fluid flow problems. This is when a stationary solution loses stability and often becomes periodic in time. The difficulty is to determine the critical Reynolds number where a pair of eigenvalues of the Jacobian matrix crosses the imaginary axis. This requires the computation of the eigenvalues (or at least some of them) of a large matrix resulting from the discretization of the incompressible Navier-Stokes equations. We thus present a method allowing the computation of the smallest eigenvalues, from which we can extract the one with the smallest real part. From the imaginary part of the critical eigenvalue we can deduce the fundamental frequency of the time-periodic solution. These computations are then confirmed by direct simulation of the time-dependent Navier-Stokes equations. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 27 Ill.
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  • 89
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1211-1223 
    ISSN: 0271-2091
    Keywords: Ekman's boundary layer ; triple deck ; non-homogeneity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem of the interaction between Ekman's classical boundary layer and that induced by a thermally non-homogeneous site shows that the latter is strongly linked to the order of magnitude of the horizontal scale of the site.Our purpose is the analysis of the local interaction equations (Boussinesq equations) starting from a triple-deck model. This analysis yields a system of quasi-linear equations for the viscous lower deck. The linear theory of this system shows that the thermal non-homogeneity has a significant influence on the Ekman boundary layer flow owing to the interactive nature of the triple-deck structure. The numerical solution of the quasi-linear system confirms to a large extent this influence. The numerical results are given in graph form. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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  • 90
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1225-1245 
    ISSN: 0271-2091
    Keywords: free surface flow ; unstructured triangular mesh ; Roe's matrix ; upwind finite volume method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A 2D, depth-integrated, free surface flow solver for the shallow water equations is developed and tested. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov-type second-order upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using Roe's flux function. The eigensystem of the 2D shallow water equations is derived and is used for the construction of Roe's matrix on an unstructured mesh. The viscous terms of the shallow water equations are computed using a finite volume formulation which is second-order-accurate. Verification of the solution technique for the inviscid form of the governing equations as well as for the full system of equations is carried out by comparing the model output with documented published results and very good agreement is obtained. A numerical experiment is also conducted in order to evaluate the performance of the solution technique as applied to linear convection problems. The presented results show that the solution technique is robust. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 11 Ill.
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  • 91
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1271-1289 
    ISSN: 0271-2091
    Keywords: viscous flow ; solidification ; electromagnetics ; finite element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Vacuum arc remelting is a process for producing homogeneous ingots of reactive and macrosegregation-sensitive alloys. A mathematical model of the transport phenomena in the ingot melt is presented together with a discussion of the various simplifying assumptions and approximations that make the problem tractable, with particular attention on transport in the interdendritic mushy zone and on the magnetohydrodynamics. The finite element method is used to discretize the equations for the non-isothermal flow problem and the quasi-static electromagnetic problem. Coupling of the finite element solutions for the two field problems is accomplished using the Parallel Virtual Machine software. An analysis of the fluid flow and heat transport in the melt pool of the solidifying ingot shows some of the factors that influence ingot quality during quasi-steady growth conditions. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
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  • 92
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1307-1319 
    ISSN: 0271-2091
    Keywords: aeroacoustics ; wind noise ; time-dependent incompressible flows ; large-eddy simulation ; acoustic boundary elements ; Helmholtz equation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite element and boundary element calculations are combined to predict the flow noise radiated from a 1/10th-scale model of an aerodynamic cover used around the pantograph on a train at 250 km h-1. The solutions of the unsteady air flow over the cover and the resulting sound propagation are divided into two parts in order to keep the problem tractable. First the unsteady fluid flow is solved using large-eddy simulation (LES). The pressure histories on the cover are then used to predict the radiated sound, using a boundary element method to solve the Helmholtz equation. The result thus leans heavily on assumptions about the coupling of the two solutions, the propagation of sound in a disturbed medium and the efficacy of LES. The predicted sound pressure levels are compared with experimental measurements made in an anechoic wind tunnel. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
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  • 93
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1353-1369 
    ISSN: 0271-2091
    Keywords: parallel computations ; parachutes ; 3D flow simulations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In the near future, large ram-air parachutes are expected to provide the capability of delivering 21 ton payloads from altitudes as high as 25,000 ft. In development and test and evaluation of these parachutes the size of the parachute needed and the deployment stages involved make high-performance computing (HPC) simulations a desirable alternative to costly airdrop tests. Although computational simulations based on realistic, 3D, time-dependent models will continue to be a major computational challenge, advanced finite element simulation techniques recently developed for this purpose and the execution of these techniques on HPC platforms are significant steps in the direction to meet this challenge. In this paper, two approaches for analysis of the inflation and gliding of ram-air parachutes are presented. In one of the approaches the point mass flight mechanics equations are solved with the time-varying drag and lift areas obtained from empirical data. This approach is limited to parachutes with similar configurations to those for which data are available. The other approach is 3D finite element computations based on the Navier-Stokes equations governing the airflow around the parachute canopy and Newton’s law of motion governing the 3D dynamics of the canopy, with the forces acting on the canopy calculated from the simulated flow field. At the earlier stages of canopy inflation the parachute is modelled as an expanding box, whereas at the later stages, as it expands, the box transforms to a parafoil and glides. These finite element computations are carried out on the massively parallel supercomputers CRAY T3D and Thinking Machines CM-5, typically with millions of coupled, non-linear finite element equations solved simultaneously at every time step or pseudo-time step of the simulation. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 24 Ill.
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  • 94
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1391-1415 
    ISSN: 0271-2091
    Keywords: meshless kernel particle method ; multiresolution analysis ; wavelets ; adaptivity ; computational fluid dynamics ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Multiresolution analysis based on the reproducing kernel particle method (RKPM) is developed for computational fluid dynamics. An algorithm incorporating multiple-scale adaptive refinement is introduced. The concept of using a wavelet solution as an error indicator is also presented. A few representative numerical examples are solved to illustrate the performance of this new meshless method. Results show that the RKPM is a good candidate for tackling the widespread large-scale problems in fluid dynamics. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
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  • 95
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 61-79 
    ISSN: 0271-2091
    Keywords: finite element ; shallow water equations ; adaptive refinement ; convergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A p-type finite element scheme is introduced for the three-dimensional shallow water equations with a harmonic expansion in time. The wave continuity equation formulation is used which decouples the problem into a Helmholtz equation for surface elevation and a momentum equation for horizontal velocity. An exploration of the applicability of p methods to this form of the shallow water problem is presented, with a consideration of the problem of continuity errors. The convergence rates and relative computational efficiency between h- and p- type methods are compared with the use of three test cases representing various degrees of difficulty. A channel test case establishes convergence rates, a continental shelf test case examines a problem with accuracy difficulties at the shelf break, and a field-scale test case examines problems with highly irregular grids. For the irregular grids, adaptive h combined with uniform p refinement was necessary to retain high convergence rates. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
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  • 96
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 151-166 
    ISSN: 0271-2091
    Keywords: convection ; shear flow ; boundary conditions ; pseudospectral ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new code for simulating convection in a horizontal layer of fluid is described. The code can be used to study the usual Rayleigh -Bénard convection problem but can also incorporate internal heating, rotation and the vortex force responsible for Langmuir circulation. Boundary conditions in the horizontal directions are periodic, but a wide range of conditions may be imposed on the upper and lower boundaries.A novel feature of the method is the way in which these boundary conditions are implemented through the following analytical/numerical technique. The governing partial differential equations are reduced to a number of inhomogeneous second-order ODEs for the horizontal Fourier modes. The solutions to these are then written as the sum of a particular integral and a complementary function. The former is easily computed (numerically) without regard to the boundary conditions and the latter is then selected (analytically/numerically) to ensure that the boundary conditions are met.We apply our code to the problem of highly supercritical thermal convection in a shear flow. We compare our results with simulations in the literature and, by integrating over a longer time interval, find flow features not observed in the previous simulations, including stable time-dependent states, multiple stable equilibria and chaos. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
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  • 97
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 167-182 
    ISSN: 0271-2091
    Keywords: Navier-Stokes procedure ; streamline co-ordinates ; QUICK scheme ; two-layer k-ε model ; CLmax ; near wake ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An accurate and robust Navier-Stokes procedure to predict the complex flow about an aerofoil has been developed. Much improvement over existing methods is achieved in various aspects of the solution procedure. The computational grid generated by conformal mapping, which is not only orthogonal but aligned with the inviscid streamlines, keeps the equations simple and minimizes the error due to false diffusion. Formal second-order accuracy is ensured by employing the QUICK scheme for the convective derivatives in the full Navier-Stokes and turbulence transport equations. To treat the separated region properly and to better resolve the flow field in the wake, the two-layer k-ε turbulence model is incorporated. The onset of transition is triggered in a unique fashion to warrant the smooth transition to turbulent flow. Sample calculations for various aerofoil sections show that the prediction is improved substantially over those by existing methods. The details of the flow extending to the wake, such as the surface pressure distribution, CLmax, the velocity fields and the Reynolds stress profiles, are found to be in excellent agreement with the data. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 15 Ill.
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  • 98
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 225-243 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; low Peclet number ; chemical vapour deposition ; low Mach number ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An enhanced solution strategy based on the SIMPLER algorithm is presented for low-Peclet-number mass transport calculations with applications in low-pressure material processing. The accurate solution of highly diffusive flows requires boundary conditions that preserve specified chemical species mass fluxes. The implementation of such boundary conditions in the standard SIMPLER solution procedure leads to degraded convergence that scales with the Peclet number. Modifications to both the non-linear and linear parts of the solution algorithm remove the slow convergence problem. In particular, the linearized species transport equations must be implicitly coupled to the boundary condition equations and the combined system must be solved exactly at each non-linear iteration. The pressure correction boundary conditions are reformulated to ensure that continuity is preserved in each finite volume at each iteration. The boundary condition scaling problem is demonstrated with a simple linear model problem. The enhanced solution strategy is implemented in a baseline computer code that is used to solve the multicomponent Navier-Stokes equations on a generalized, multiple-block grid system. Accelerated convergence rates are demonstrated for several material-processing example problems. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 17 Ill.
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  • 99
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    International Journal for Numerical Methods in Fluids 25 (1997), S. 393-405 
    ISSN: 0271-2091
    Keywords: multigrid methods ; pressure correction methods ; incompressible Navier-Stokes equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We compare the performance of different pressure correction algorithms used as basic solvers in a multigrid method for the solution of the incompressible Navier-Stokes equations on non-staggered grids. Numerical tests were performed on several cases of lid-driven cavity flow using four different pressure correction schemes, including the traditional SIMPLE and SIMPLEC methods as well as novel variants, and varying combinations of underrelaxation parameters. The results show that three of the four algorithms tested are robust smoothers for the multigrid solver and that one of the new methods converges fastest in most of the tests. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
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  • 100
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    International Journal for Numerical Methods in Fluids 24 (1997), S. 1129-1158 
    ISSN: 0271-2091
    Keywords: spectral finite difference ; direct numerical simulation ; message-passing computers ; data partitioning ; fractional step methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method for efficient implementation of a combined spectral finite difference algorithm for computation of incompressible stratified turbulent flows on distributed memory computers is presented. The solution technique is the fractional step method with a semi-implicit time advancement scheme. A single-programme multiple-data abstraction is used in conjunction with a static data-partitioning scheme. The distributed FFTs required in the explicit step are based on the transpose method and the large sets of independent tridiagonal systems of equations arising in the implicit steps are solved using the pipelined Thomas algorithm. A speed-up analysis of a model problem is presented for three partitioning schemes, namely unipartition, multipartition and transpose partition. It is shown that the unipartitioning scheme is best suited for this algorithm. Performance measurements of the overall as well as individual stages of the algorithm are presented for several different grids and are discussed in the context of associated dependency and communication overheads. An unscaled speed-up efficiency of up to 91% on doubling the number of processors and up to 60% on an eightfold increase in the number of processors was obtained on the Intel Paragon and iPSC/860 Hypercube. Absolute performance of the code was evaluated by comparisons with performance on the Cray-YMP. On 128 Paragon processors, performance up to five times that of a single-processor Cray-YMP was obtained. The validation of the method and results of grid refinement studies in stably stratified turbulent channel flows are presented. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 20 Ill.
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