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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 515-548 
    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; contravariant velocities ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To analyse an incompressible Navier-Stokes flow problem in a boundary- fitted curvilinear co-ordinate system is definitely not a trivial task. In the primitive variable formulation, choices between working variables and their storage points have to be made judiciously. The present work engages contravariant velocity components and scalar pressure which stagger each other in the mesh to prevent even-odd pressure oscillations from emerging. Now that smoothness of the pressure field is attainable, the remaining task is to ensure a discrete divergence-free velocity field for an incompressible flow simulation. Aside from the flux discretizations, the indispensable metric tensors, Jacobian and Christoffel symbols in the transformed equations should be approximated with care. The guiding idea is to get the property of geometric identity pertaining to these grid-sensitive discretizations. In addition, how to maintain the revertible one-to-one equivalence at the discrete level between primitive and contravariant velocities is another theme in the present staggered formulation. A semi-implicit segregated solution algorithm felicitous for a large-scale flow simulation was utilized to solve the entire set of basic equations iteratively. Also of note is that the present segregated solution algorithm has the virtue of requiring no user-specified relaxation parameters for speeding up the satisfaction of incompressibility in an optimal sense. Three benchmark problems, including an analytic problem, were investigated to justify the capability of the present formulation in handling problems with complex geometry. The test cases considered and the results obtained herein make a useful contribution in solving problems subsuming cells with arbitrary shapes in a boundary-fitted grid system.
    Additional Material: 21 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 619-641 
    ISSN: 0271-2091
    Keywords: convective transport ; monotonicity ; finite volume ; boundary-fitted co-ordinates ; turbulence modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A formally third-order accurate finite volume upwind scheme which preserves monotonicity is constructed. It is based on a third-order polynomial interpolant in Leonard's normalized variable space. A flux limiter is derived using the fact that there exists a one-to-one map between normalized variable and TVD spaces. This scheme, which is relatively simple and quite compact, is implemented in a staggered general co-ordinates finite volume algorithm including the standard k-ε model and applied to the turbulence transport equations. A number of test problems demonstrate the utility of the proposed scheme. It is shown that in cases where turbulence convection is dominant, the application of a higher-order monotone convection scheme to the turbulence equations leads to results which are more accurate than those obtained using the first-order upwind scheme.
    Additional Material: 21 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 673-688 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; projection methods ; operator splitting ; spectral element methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An approximate projection scheme based on the pressure correction method is proposed to solve the Navier-Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward-facing step.
    Additional Material: 6 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 755-770 
    ISSN: 0271-2091
    Keywords: Stokes ; multigrid ; Krylov subspace ; conjugate gradient ; conjugate residual ; Uzawa ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper we compare the performance of four such methods, namely variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual and multigrid methods, for solving several two-dimensional model problems. The results indicate that multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being independent of iteration parameters.
    Additional Material: 5 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 799-810 
    ISSN: 0271-2091
    Keywords: jets ; jet impingement ; turbulence ; k-ε model ; finite volume method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper reports numerical modelling of impinging jet flows using Rodi and Malin corrections to the k-ε turbulence model, carried out using the PHOENICS finite volume code. Axisymmetric calculations were performed on single round free jets and impinging jets and the effects of pressure ratio, height and nozzle exit velocity profile were investigated numerically. It was found that both the Rodi and Malin corrections tend to improve the prediction of the hydrodynamic field of free and impinging jets but still leave significant errors in the predicted wall jet growth. These numerical experiments suggest that conditions before impingement significantly affect radial wall jet development, primarily by changing the wall jet's initial thickness.
    Additional Material: 11 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 771-798 
    ISSN: 0271-2091
    Keywords: curved pipe flow ; variable cross-section ; secondary flow ; artery ; Engineering ; Engineering General
    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 steady, laminar flow of an incompressible Newtonian fluid in curved pipes of non-uniform cross-section. During the past decade a number of numerical solutions for flow in curved pipes have been obtained using progressively improved computational methods and technology; see e.g. Soh and Berger (Int. j. numer. methods fluids, 7, 733-755 (1987)) and Green et al. (Phil. Trans. R. Soc. Lond. A, 342, 543-572 (1993)) for relevant references. These results have been confined mainly to fully developed flow in pipes of constant cross-section. The present study deals with curved pipes of variable cross-section in which the velocity field is necessarily a function of the axial location along the pipe centreline in addition to the two cross-sectional co-ordinates. We use the finite difference method on a staggered grid with Newton's method to solve the Navier-Stokes equations. Results are calculated and presented for non-uniform pipe geometries with curvature ratios of 0ċ01 and 0ċ1. The velocity field for flow through curved pipes of non-uniform cross-section is compared with the corresponding results for flow through straight pipes of non-uniform radius and curved pipes of uniform radius, revealing important qualitative differences. The basic developments presented are applicable to a variety of flows in pipes, including those in arteries and piping systems.
    Additional Material: 14 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 835-849 
    ISSN: 0271-2091
    Keywords: non-linear first-order hyperbolic system ; collocation method ; upwinding ; thermal pipeline simulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Simulating thermal effects in pipeline flow involves solving a coupled non-linear system of first-order hyperbolic equations. The advection term has two large eigenvalues of opposite signs, corresponding to the propagation of high-speed sound waves, and one eigenvalue close to or even equal to zero, representing the much slower fluid flow velocity, which transports temperature. Standard collocation methods work well for isothermal flow in pipelines, but the stagnating eigenvalue causes difficulties when thermal effects are included. In a companion paper we formulate and analyse a new numerical method for the non-linear system which arises in thermal modelling. The new method applies to general coupled systems of non-linear first-order hyperbolic partial differential equations with one degenerate eigenvalue. In the present paper we focus on a linearized constant coefficient form of the thermal flow equations. This substantially simplifies presentation of the error analysis for the numerical scheme. We also include numerical results for the method applied to the fully non-linear system. Both the error analysis and the numerical experiments show that the difficulties that come from the application of standard collocation can be overcome by using upwinded piecewise constant functions for the degenerate component of the solution.
    Additional Material: 4 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 881-897 
    ISSN: 0271-2091
    Keywords: turbine cascade flows ; vortex shedding (periodic flows) ; compressible viscous flows ; turbulence and transition ; boundary layers ; multiblock meshes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Periodic vortex shedding at the trailing edge of a turbine cascade has been investigated numerically for a subsonic and a transonic cascade flow. The numerical investigation was carried out by a finite volume multiblock code, solving the 2D compressible Reynolds-averaged Navier-Stokes equations on a set of non-overlapping grid blocks that are connected in a conservative way. Comparisons are made with experimental results previously obtained by Sieverding and Heinemann.
    Additional Material: 14 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 549-565 
    ISSN: 0271-2091
    Keywords: parallel computing ; multigrid method ; finite volume method ; block-structured grids ; incompressible flow ; Engineering ; Engineering General
    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 a parallel multigrid finite volume solver for the prediction of steady and unsteady flows in complex geometries is presented. For the handling of the complexity of the geometry and for the parallelization a unified approach connected with the concept of block-structured grids is employed. The parallel implementation is based on grid partitioning with automatic load balancing and follows the message-passing concept, ensuring a high degree of portability. A high numerical efficiency is obtained by a non-linear multigrid method with a pressure correction scheme as smoother.By a number of numerical experiments on various parallel computers the method is investigated with respect to its numerical and parallel efficiency. The results illustrate that the high performance of the underlying sequential multigrid algorithm can largely be retained in the parallel implementation and that the proposed method is well suited for solving complex flow problems on parallel computers with high efficiency.
    Additional Material: 11 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 581-601 
    ISSN: 0271-2091
    Keywords: unstructured grids ; incompressible viscous flow ; pressure-correction method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An unstructured grid, finite volume method is presented for the solution of two-dimensional viscous, incompressible flow. The method is based on the pressure-correction concept implemented on a semi-staggered grid. The computational procedure can handle cells of arbitrary shape, although solutions presented herein have been obtained only with meshes of triangular and quadrilateral cells. The discretization of the momentum equations is effected on dual cells surrounding the vertices of primary cells, while the pressure-correction equation applies to the primary-cell centroids and represents the conservation of mass across the primary cells. A special interpolation scheme s used to suppress pressure and velocity oscillations in cases where the semi-staggered arrangement does not ensure a sufficiently strong coupling between pressure and velocity to avoid such oscillations. Computational results presented for several viscous flows are shown to be in good agreement with analytical and experimental data reported in the open literature.
    Additional Material: 17 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 713-729 
    ISSN: 0271-2091
    Keywords: finite difference ; boundary conditions ; Navier-Stokes equations ; convergence analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference method for the Navier-Stokes equations in vorticity -streamfunction formulation is proposed to resolve the difficulty of the lack of a vorticity boundary condition at a no-slip boundary. It is particularly suitable for flows in regions with complicated geometries. Convergence with second-order accuracy in vorticity and velocity is established. In numerical experiments the convergence rates agree with theoretical predictions. Test results for the two-dimensional driven cavity problem and for the flow in expansion and contraction channels are given.
    Additional Material: 4 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 691-712 
    ISSN: 0271-2091
    Keywords: ELAFINT ; interface tracking ; solidification ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this work a mixed Eulerian-Lagrangian technique is devised, hereinafter abbreviated as ELAFINT (Eulerian-Lagrangian Algorithm For INterface Tracking). The method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving/free phase boundaries. The position and shape of the boundary are tracked explicitly by the Lagrangian translation of marker particles. The field equations are solved on an underlying fixed grid as in Eulerian methods. The interface passes through the grid lay-out and details regarding the treatment of the cut cells so formed are provided. The issues involved in treating the internal boundaries are dealt with, with particular attention to conservation and consistency in the vicinity of the interface. The method is tested by comparing with solutions from well-tested body-fitted co-ordinate methods. Test cases pertaining to forced and natural convection in irregular geometries and moving phase boundaries with melt convection are presented. The capability developed here can be beneficial in solving difficult flow problems involving moving and geometrically complex boundaries.
    Additional Material: 18 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 149-150 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 867-879 
    ISSN: 0271-2091
    Keywords: optimal control ; optimization ; gas pipelines ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A general optimal control approach employing the principles of calculus of variations has been developed to determine the best operating strategies for keeping the outlet pressure of gas transmission pipelines around a predetermined value while achieving reasonable energy consumption. The method exploits analytical tools of optimal control theory. A set of partial differential equations characterizing the dynamics of gas flow through a pipeline is directly used. The necessary conditions to minimize the specific performance index come from the infinite-dimensional model. The optimization scheme has been tested on a pipeline subject to stepwise change in demand.
    Additional Material: 11 Ill.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 915-917 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 919-919 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 211-221 
    ISSN: 0271-2091
    Keywords: backward-facing step ; particle-laden flow ; Lagrangian tracking ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Particle-laden flows are calculated for a classical laminar backward- facing step problem. The particle tracks are calculated using a recently developed exponential Lagrangian tracking scheme. The behaviour of the particle-laden flow is considered for various inlet for Reynolds number, Stokes numbers and void fractions. Doping the flow with low-Stokes-number particles has the effect of increasing the inlet inertia of the flow and this increases the strength of the recirculation behind the step. High-Stokes- number particles are dominated by gravitational effects which affect the flow accordingly. Differences between the single-phase flow and the particle-laden flows are therefore dependent on the Stokes number and increase linearly with void fraction.
    Additional Material: 9 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 225-240 
    ISSN: 0271-2091
    Keywords: domain decomposition ; line Gauss-Seidel ; conjugate gradient ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical discretization of the equations governing fluid flow results in coupled, quasi-linear and non-symmetric systems. Various approaches exist for resolving the non-linearity and couplings. During each non-linear iteration, nominally linear systems are solved for each of the flow variables. Line relaxation techniques are traditionally employed for solving these systems. However, they could be very expensive for realistic applications and present serious synchronization problems in a distributed memory parallel environment. In this paper the discrete linear systems are solved using the generalized conjugate gradient method of Concus and Golub. The performance of this algorithm is compared with the line Gauss-Seidel algorithm for laminar recirculatory flow in uni- and multiprocessor environments. The uniprocessor performances of these algorithms are also compared with that of a popular iterative solver for non-symmetric systems (the GMRES algorithm).
    Additional Material: 8 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 283-296 
    ISSN: 0271-2091
    Keywords: laminar flow ; numerical modelling ; particle image velocimetry measurement ; rotating disc ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The fluid flow field within an enclosed cylindrical chamber with a rotating flat disc was calculated using a finite volume computational fluid dynamics (CFD) model and compared with particle image velocimetry (PIV) measurements. Two particular laminar cases near the Transitional flow regime were investigated: Reynolds number Re=2.5×1 4, chamber aspect ratio G (h/Rd)=0.2 and Re=4.2×104, G (h/Rd)=0.217. This enabled direct comparison with the numerical and experimental results reported by other researchers. The computational details and some major factors that affect the computed accuracy and convergence speed are also discussed in detail. PIV results containing some 4300 velocity vector points in each of seven planes for each case were obtained from the flow field parallel to the rotating disc. It was found that PIV results could be obtained in planes within the boundary layers as well as the core flow by careful use of a thin laser illumination sheet and correct choice of laser pulse separation. There was close agreement between numerical results, the present PIV measurements and other reported experimental and numerical results.
    Additional Material: 10 Ill.
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 297-311 
    ISSN: 0271-2091
    Keywords: large-eddy simulation ; numerical schemes ; mixing layer ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A posteriori tests of large-eddy simulations for the temporal mixing layer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tensor. The results of the large-eddy simulations are compared with filtered direct numerical simulation (DNS) results. Five numerical methods are considered. The cell vertex scheme (A) is a weighted second-order central difference. The transverse weighting is shown to be necessary, since the standard second-order central difference (A′) gives rise to instabilities. By analogy, a new weighted fourth-order central difference (B) is constructed in order to overcome the instability in simulations with the standard fourth-order central method (B′). Furthermore, a spectral scheme (C) is tested. Simulations using these schemes have been performed for the case where the filter width equals the grid size (I) and the case where the filter width equals twice the grid size (II). The filtered DNS results are best approximated in case II for each of the numerical methods A, B and C. The deviations from the filtered DNS data are decomposed into modelling error effects and discretization error effects. In case I the absolute modelling error effects are smaller than in case II owing to the smaller filter width, whereas the discretization error effects are larger, since the flow field contains more small-scale contributions. In case I scheme A is preferred over scheme B, whereas in case II the situation is the reverse. In both cases the spectral scheme C provides the most accurate results but at the expense of a considerably increased computational cost. For the prediction of some quantities the discretization errors are observed to eliminate the modelling errors to some extent and give rise to reduced total errors.
    Additional Material: 3 Ill.
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  • 24
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 375-392 
    ISSN: 0271-2091
    Keywords: gates ; finite elements ; potential flow ; free surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional finite element analyses of two types of gate - (i) a conduit gate with pressure flow upstream of the gate and free surface flow downstream of the gate and (ii) a sluice gate with free surfaces both upstream and downstream of the gate - are done using ideal fluid theory. The conduit gate problem is solved using both Φ- and Ψ- formulations. Various methods of satisfying the boundary conditions were tested for both formulations. The ψ-formulation developed in the present study is found to converge faster for flows with Froude numbers less than 4, which are common in sluice gates. The results obtained from the present study are compared with results from analytical and experimental techniques available in the literature. The ψ-formulation developed in the present study is then used to solve the spillway gate problem, for which no analytical solution is available.
    Additional Material: 14 Ill.
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 411-428 
    ISSN: 0271-2091
    Keywords: composite grids ; adaptive grids ; multigrid parallelization ; Euler ; implicit scheme ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method capable of solving very fast and robust complex non-linear systems of equations is presented. The block adaptive multigrid (BAM) method combines mesh adaptive techniques with multigrid and domain decomposition methods. The overall method is based on the FAS multigrid, but instead of using global grids, locally enriched subgrids are also employed in regions where excessive solution errors are encountered. The final mesh is a composite grid with uniform rectangular subgrids of various mesh densities. The regions where finer grid resolution is necessary are detected using an estimation of the solution error by comparing solutions between grid levels. Furthermore, an alternative domain decomposition strategy has been developed to take advantage of parallel computing machines. The proposed method has been applied to an implicit upwind Euler code (EuFlex) for the solution of complex transonic flows around aerofoils. The efficiency and robustness of the BAM method are demonstrated for two popular inviscid test cases. Up to 19-fold acceleration with respect to the single-grid solution has been achieved, but a further twofold speed-up is possible on four-processor parallel computers.
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  • 26
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 449-465 
    ISSN: 0271-2091
    Keywords: aeroacoustic ; vortex shedding ; solid rocket motor ; implicit or explicit method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The present work is devoted to the numerical simulation of two important phenomena in the field of solid propellant rocket motors: the first is acoustic boundary layers that develop above the burning propellant; the other is a periodic vortex-shedding phenomenon which is the result of a strong coupling between the instability of mean flow shear layers and acoustic motions in the chamber. To predict the acoustic boundary layer, computations were performed for the lower half of a rectangular chamber with bottom-side injection. The outflow pressure is sinusoidally perturbed at a given frequency. For the highest CFL numbers the implicit scheme is not able to compute the unsteadiness in the acoustic boundary layer. With very low CFL numbers or with the explicit scheme the main features of the acoustic field are captured. To simulate the vortex-shedding mechanismin a segmented solid rocket motor, the explicit version is used. This computation shows a mechanism for ‘self-excited’ vortex shedding close to the second axial mode frequency. The use of the flux-splitting technique reduces substantially the amplitude of the oscillations. A few iterations are done with flux splitting, then the computation is performed without this technique. In this case both the frequency and the intensity are well predicted. A geometry more representative of the solid rocket motor is also computed. In this case the vortex-shedding process is more complex and pairing is observed.
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  • 27
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 28
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 307-308 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 29
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 569-580 
    ISSN: 0271-2091
    Keywords: magnetohydrodynamics ; Godunov ; upwind ; conservative ; plasma ; fusion ; Engineering ; Engineering General
    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 a higher-order Godunov method for one-dimensional solutions of the ideal MHD (magneto-hydrodynamics) equations is presented. The method uses a fluctuation approach and includes a new sonic fix and a new Roe averaging. After a short introduction the MHD equations in conservative form are given. The flux is rearranged such that the eigenstructure is not changed. This rearrangement allows full Roe averaging for any value of adiabatic index (contrary to Brio and Wu's conclusion). A new procedure to get Roe - averaged MHD fields at the interfaces between left and right states is then presented and some useful identities are given. Next the second-order-limited fluctuation approach is presented in full detail. The new sonic fix for MHD and the procedure for applying this fix to the sonic points are then given in detail. Numerical results obtained with the described method are presented. Finally, conclusions are given.
    Additional Material: 4 Ill.
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  • 30
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 31
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 397-411 
    ISSN: 0271-2091
    Keywords: GMRES ; mild slope equation ; iterative solvers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The mild slope equation in its linear and non-linear forms is used for the modelling of nearshore wave propagation. The finite difference method is used to descretize the governing elliptic equations and the resulting system of equations is solved using GMRES-based iterative method. The original GMRES solution technique of Saad and Schultz is not directly applicable to the present case owing to the complex coefficient matrix. The simpler GMRES algorithm of Walker and Zhou is used as the core solver, making the upper Hessenberg factorization unneccessary when solving the least squares problem. Several preconditioning-based acceleration strategies are tested and the results show that the GMRES-based iteration scheme performs very well and leads to monotonic convergence for all the test-cases considered.
    Additional Material: 10 Ill.
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  • 32
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 455-466 
    ISSN: 0271-2091
    Keywords: computational fluid dynamics ; unsteady incompressible flow ; method of lines ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A novel approach to the development of a code for the solution of the time-dependent two-dimensional Navier-Stokes equations is described. The code involves coupling between the method of lines (MOL) for the solution of partial differential equations and a parabolic algorithm which removes the necessity of iterative solution on pressure and solution of a Poisson-type equation for the pressure. The code is applied to a test problem involving the solution of transient laminar flow in a short pipe for an incompressible Newtonian fluid. Comparisons show that the MOL solutions are in good agreement with the previously reported values. The proposed method described in 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).
    Additional Material: 5 Ill.
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  • 33
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 485-501 
    ISSN: 0271-2091
    Keywords: shallow recirculating flow ; multilayer model ; turbulence model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A quasi-three-dimensional multilayer k- ∊ model has been developed to simulate turbulent recirculating flows behind a sudden expansion in shallow waters. The model accounts for the vertical variation in the flow quantities and eliminates the problem of closure for the effective stresses resulting from the depth integration of the non-linear convective accelerations found in the widely used depth- integrated models. The governing equations are split into three parts in the finite difference solution: advection, dispersion and propagation. The advection part is solved using the four-node minimax-characteristics method. The dispersion and propagation parts are treated by the central difference method, the former being solved explicitly and the latter implicitly using the Gauss-Seidel iteration method. The relative effect of bed-generated turbulence and transverse shear-generated turbulence on the recirculating flow has been studied in detail. In comparison with the results computed by the depth-integrated k-∊ model, the results computed by the present model are found to be closer to the reported data.
    Additional Material: 12 Ill.
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  • 34
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 861-863 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 35
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 811-813 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 36
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 815-834 
    ISSN: 0271-2091
    Keywords: vertical discretization ; sigma co-ordinates ; localized sigma co-ordinates ; tidal flow ; numerical experimentation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We propose an empirical law for vertical nodal placement in tidal simulations that depends on a single parameter p. The influence of dimensionless numbers on the optimal value of pis analysed through a series of numerical experiments for an individual vertical and a single value of pis found to be adequate for all cases. The proposed law can lead to gains in accuracy of over two orders of magnitude relative to a uniform grid and compares favourably with non-uniform grids previously used in the literature. In practical applications the most effective use of this law may require each vertical to have a different number of nodes. Criteria for the distribution of the total number of nodes among different verticals are also proposed, based on the concept of equalizing errors across the domain. The usefulness of the overall approach is demonstrated through a two-dimensional laterally averaged application to a synthetic estuary.
    Additional Material: 15 Ill.
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  • 37
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 851-865 
    ISSN: 0271-2091
    Keywords: surface tension ; free boundary ; moving boundary ; implied algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: One of the methods for solving a free or moving boundary problem is the use of Picard solvers which solve the geometry and the velocity field successively. When, however, the kinematic condition is used for updating the geometry in this technique, numerical stability problems occur for surface-tension-dominated flow. These problems are shown here to originate from the unstable integration of the local smoothing of the surface by surface tension. By an extension of the surface tension contribution to the flow field an implicit treatment of surface tension is obtained which overcomes these stability problems. The algorithm is applicable to both free and moving boundary problems, as will be shown by examples in this paper.
    Additional Material: 7 Ill.
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  • 38
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 899-913 
    ISSN: 0271-2091
    Keywords: grid generation ; tri-tree ; unstructured grid ; finite elements ; mixed formulation ; analytic integration ; adaptive solver ; Stokes equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An iterative adaptive equation solver for solving the implicit Stokes equations simultaneously with tri-tree grid generation is developed. The tri-tree grid generator builds a hierarchical grid structure which is mapped to a finite element grid at each hierarchical level. For each hierarchical finite element grid the Stokes equations are solved. The approximate solution at each level is projected onto the next finer grid and used as a start vector for the iterative equation solver at the finer level. When the finest grid is reached, the equation solver is iterated until a tolerated solution is reached.In order to reduce the overall work, the element matrices are integrated analytically beforehand. The efficiency and behaviour of the present adaptive method are compared with those of the previously developed iterative equation solver which is preconditioned by incomplete LU factorization with coupled node fill-in.The efficiency of the incomplete coupled node fill-in preconditioner is shown to be largely dependent on the global node numbering. The preconditioner is therefore tested for the natural node ordering of the tri-tree grid generator and for different ways of sorting the nodes.
    Additional Material: 7 Ill.
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  • 39
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 921-935 
    ISSN: 0271-2091
    Keywords: two-phase flow ; multilevel ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A time-dependent numerical algorithm is developed for the two-fluid model Euler of TLNS (thin layer Navier-Stokes) equations. The analysis is based on a MUSCL (monotone upstream central scheme for conservation laws)-type flux-vector-splitting scheme with the multi-level technique. This algorithm is applied to investigate JPL (Jet Propulsion Laboratory) nozzle flow. Calculated results for both one- and two-phase flows are given to show the accuracy, the computational efficiency and the particle influence on the flow field.
    Additional Material: 15 Ill.
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  • 40
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 1133-1144 
    ISSN: 0271-2091
    Keywords: turbulence models ; realizability ; complex flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Various wall-bounded flows with complex geometries and free shear flows have been studied with a newly developed realizable Reynolds stress algebraic equation model. The model development is based on the invariant theory in continuum mechanics. This theory enables us to formulate a general constitutive relation for the Reynolds stresses. Pope (J. Fluid Mech., 72, 331-340 (1975)) was the first to introduce this kind of constitutive relation to turbulence modelling. In our study, realizability is imposed on the truncated constitutive relation to determine the coefficients so that, unlike the standard k-∊ eddy viscosity model, the present model will not produce negative normal stresses in any situations of rapid distortion. The calculations based on the present model have shown encouraging success in modelling complex turbulent flows.
    Additional Material: 15 Ill.
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  • 41
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 1197-1210 
    ISSN: 0271-2091
    Keywords: finite element method ; gust ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In the structural design of civil aircraft the critical loads are often those encountered in a gust or atmospheric turbulence. The traditional ‘indicial’ solution is restricted to a simple plate. In this paper a finite element formulation is proposed for an aerofoil or arbitrary shape entering a uniform sharp-edged or sinusoidal gust. The thin rotational gust front and wake in an irrotational flow field are successfully modelled by a novel superposition technique. The finite element solutions are compared with the Kussner function and results by other numerical methods. The agreement is good.
    Additional Material: 16 Ill.
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  • 42
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 1235-1235 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 43
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 1275-1287 
    ISSN: 0271-2091
    Keywords: Dean vortices ; system rotation ; Eckhaus instability ; centrifugal and coriolis forces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Three-dimensional spatially developing Navier-Stokes calculations are carried out to simulate the flow in a curved, rotating channel. The competition between centrifugal and Coriolis forces, expressed by the ratio of the Dean number to the rotation number, gives rise to a variety of possible instability modes characterized by the presence of streamwise vortices. Cases in which the force produced by system rotation enhances or opposes the centrifugal force are treated and the effect on the ensuing instability are analysed. Evidence for a generalized Eckhaus instability of rotating Dean vortices is presented.
    Additional Material: 10 Ill.
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  • 44
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 1241-1262 
    ISSN: 0271-2091
    Keywords: axisymmetric flow ; vortex method ; laminar flow ; entrance length ; steady and oscillating flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steady and oscillating axisymmetric tube flows are modelled using a vorticity transport algorithm. The axisymmetric convective -diffusive Navier-Stokes equations are solved using a splitting technique. Axisymmetric ring vortex filaments are introduced on the walls and subsequently convected and diffused throughout the flow field. An axisymmetric equation similar to the Oseen diffusion equation is used to diffuse the ring vortex filaments. Vorticity is reflected from the tube walls using two techniques. Results are presented for the developing Poiseuille flow and for the developed flow in the form of the entrance length and the axial velocity and vorticity profiles. Good agreement is achieved with a finite difference method in the developing region of Poiseuille flow. The developed flow results are compared with the analytical solutions. The developed profiles of velocity and vorticity have errors of less than 0ċ3 per cent for both methods of dealing with reflection of diffusion at the bounding surfaces and similar accuracy is obtained for the velocity profiles in oscillating flow except at the wall. Oscillating flow is produced with a discretized sinusoidal piston motion. Velocity profiles, boundary layer thickness and entrance length are presented for oscillating flow. Good agreement is achieved for low-Womersley-number non-dimensional frequency. At higher values of this parameter, flows are inaccurately simulated, because the number of piston positions used to discretize the piston motion is inversely proportional to the non-dimensional frequency.
    Additional Material: 19 Ill.
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  • 45
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 1347-1347 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 46
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 711-732 
    ISSN: 0271-2091
    Keywords: finite difference scheme ; prowake co-ordinates ; vorticity conditioning ; high-order upwinding ; semi-explicit time marching ; bluff object ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A semi-explicit finite difference scheme is proposed to study unsteady two-dimensional, incompressible flow past a bluff object at high Reynolds number. The bluff object comes from a class of elliptical cylinders in which the aspect ratio and the angle of attack are two controlled parameters. Associated with the streamfunction-vorticity formulation, the interior vorticity, streamfunction and wall vorticity are updated in turn for each time step. The streamfunction and wall vorticity are solved by means of a multigrid method and a projection method respectively. In regard to the vorticity transport equation, implicitness is merely associated with the diffusion operator, which can be made semi-explicit via approximate factorization. Low-diffusive upwinding is devised to handle the convection part. Numerical results are reported for Reynolds numbers up to 40,000. Comparisons with other numerical or physical experiments are included.
    Additional Material: 19 Ill.
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  • 47
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 637-660 
    ISSN: 0271-2091
    Keywords: wave-body interaction ; integral equation ; irregular frequency ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical techniques for the analysis of wave-body interactions are developed by the combined use of two boundary integral equation formulations. The velocity potential, which is expressed in a perturbation expansion, is obtained directly from the application of Green's theorem (the ‘potential formulation’), while the fluid velocity is obtained from the gradient of the alternative form where the potential is represented by a source distribution (the ‘source formulation’). In both formulations, the integral equations are modified to remove the effect of the irregular frequencies.It is well known from earlier works that if the normal velocity is prescribed on the interior free surface, inside the body, an extended boundary integral equation can be derived which is free of the irregular frequency effects. It is shown here that the value of the normal velocity on the interior free surface must be continuous with that outside the body, to avoid a logarithmic singularity in the source strength at the waterline. Thus the analysis must be carried out sequentially in order to evaluate the fluid velocity correctly: first for the velocity potential and then for the source strength.Computations are made to demonstrate the effectiveness of the extended boundary integral euations in the potential and source formulations. Results are shown which include the added-mass and damping coefficients and the first-order wave-exciting forces for simple three-dimensional bodies and the second-order forces on a tension-leg-platform. The latter example illustrates the importance of removing irregular frequency effects in the context of second-order wave loads.
    Additional Material: 11 Ill.
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  • 48
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 787-809 
    ISSN: 0271-2091
    Keywords: operator-splitting ; general algorithm ; characteristic-Galerkin ; laminar/turbulent ; incompressible ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In an earlier paper, Zienkiewicz and Codina (Int. j. numer. methods fluids, 20, 869-885 (1995)) presented a general algorithm for the solution of both compressible and incompressible Navier-Stokes equations. The algorithm, based on operator splitting, permits arbitrary interpolation functions to be used while avoiding the Babŭska-Brezzi restriction. In addition, its characteristic based approach introduces a form of rational dissipation. Zienkiewicz et al. (Int. j. numer. methods fluids, 20, 887-913 (1995)) presented the application of this algorithm in its fully explicit form to various inviscid compressible flow problems. They also presented two incompressible flow problems solved by the fully explicit form, employing a pseudo compressibility. The present work deals with the application of the above algorithm it its semi-implicit form to some incompressible flow benchmark problems. Further, it extends the methodology to turbulent flows by employing both one, and two equation turbulence models. A comparison of results with earlier investigations is presented. Other issues addressed in this study include the effect of additional diffusion terms present in the scheme for both laminar and turbulent flow problems and some practical difficulties associated with local time stepping.
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  • 49
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 859-859 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 50
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 819-846 
    ISSN: 0271-2091
    Keywords: shallow water equations ; boundary-fitted co-ordinate systems ; curvilinear meshes ; finite difference method ; conformal mapping ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications.
    Additional Material: 24 Ill.
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  • 51
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 883-895 
    ISSN: 0271-2091
    Keywords: N-S solver ; Turbomachinery ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The internal flows inside a backswept centrifugal impeller at off-design point conditions are analysed by solving the fully three- dimensional Navier-Stokes equations coupled with the k-∊ two-equation turbulence model. Conditions analysed have flow rates of 85 per cent and 113 per cent of the design rate. The calculated results are compared with published experimental data and the comparison shows good agreement. A jet wake structure occurs near the outlet of the impeller for each of the two off-design flow rates and the location and size of the jet wake structure seem to be independent of the flow rate.
    Additional Material: 13 Ill.
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  • 52
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 991-1020 
    ISSN: 0271-2091
    Keywords: finite element analysis ; design sensitivity analysis ; optimization ; contraction design ; Engineering ; Engineering General
    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 and the Newton-Raphson solution algorithm are combined to solve the momentum, mass and energy conservation equations for coupled flow problems. Design sensitivities for a generalised response function with respect to design parameters which describe shape, material property and load data are evaluated via the direct differentiation method. The efficiently computed sensitivities are verified by comparison with computationally intensive, finite difference sensitivity approximations. The design sensitivities are then used in a numerical optimization algorithm to minimize the pressure drop in flow through contractions. Both laminar and turbulent flows are considered. In the turbulent flow problems the time-averaged momentum and mass conservati on equations are solved using a mixing length turbulence model.
    Additional Material: 12 Ill.
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  • 53
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    International Journal for Numerical Methods in Fluids 23 (1996), S. 1043-1072 
    ISSN: 0271-2091
    Keywords: lee-waves ; seamount ; turbulence-energy ; mixing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A three-dimensional, primitive equation, baroclinic numerical model incorporating a range of turbulence energy submodels is used to study the generation of internal lee waves over an isolated seamount. Attention is given to the turbulence mixing enhanced by the internal lee waves. The results show that regions of strong turbulence energy appear over the lee side of the seamount associated with the production of the lee waves. The computed vertical eddy viscosity and diffusivity using turbulence models can be as large as 1 m2s-1.A comparison of the magnitude and spatial distribution of the internal lee waves does not reveal any major differences in results computed using different turbulence energy models or mixing determined from a Richards on number formulation. However, the magnitude of the vertical mixing is sensitive to the form of turbulence energy submodel. Also, a study of the relevant importance of the various terms in the turbulence energy equation shows that the term representing the advection of turbulence needs to be retained in order to accurately reproduce the mixing produced by the internal lee waves. Calculations using a range of seamount profiles show that the magnitude of near-bed turbulence is sensitive to the shape of the seamount.The magnitude and spatial distribution of the lee waves and associated flow field are affected by the parametrization of horizontal diffusion, with significant differences between the use of Laplacian and biharmonic forms of horizontal diffusion. The application of biharmonic horizontal diffusion is recommended.
    Additional Material: 20 Ill.
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  • 54
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 55
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 67-79 
    ISSN: 0271-2091
    Keywords: Karhunen-Loéve decomposition ; turbulent thermal convection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Karhunen-Loéve (K-L) procedure is applied to a turbulent thermal convection database which is generated numerically through integration of the Boussinesq equation in a periodic box with stress-free boundary conditions using a Fourier collocation spectral method. This procedure generates a complete set of mutually orthogonal functions in terms of which the turbulent flow fluctuation field is represented optimally in the mean square sense. A study is performed ranging from the direct projection of the database onto the set, resulting in a considerable data compression, to developing a system of dynamical equations employing the set as a basis for approximating the Boussinesq equation. In the latter a new strategy is proposed and tested for the treatment of the mean component of the turbulent flow. Finally, the direct projection and the dynamical equations are used to study the effects of truncation on the representation of the turbulent flow.
    Additional Material: 6 Ill.
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  • 56
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 325-352 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; artificial boundary conditions ; flux and pressure conditions ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Fluid dynamical problems are often conceptualized in unbounded domains. However, most methods of numerical simulation then require a truncation of the conceptual domain to a bounded one, thereby introducing artificial boundaries. Here we analyse our experience in choosing artificial boundary conditions implicitly through the choice of variational formulations. We deal particularly with a class of problems that involve the prescription of pressure drops and/or net flux conditions.
    Additional Material: 19 Ill.
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  • 57
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 58
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 393-409 
    ISSN: 0271-2091
    Keywords: generalized Stokes problem ; Chebyshev spectral method ; thermosolutal convection ; directional solidification ; vertical Bridgman problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper presents a Chebyshev-Fourier collocation method for solving the unsteady 3D Navier-Stokes equations in a cylindrical domain. The numerical scheme uses primitive variables and the incompressibility constraint is satisfied by applying iteratively a correction to the pressure field. The method, due to Cahouët and Chabard (Int. j. numer. methods fluids,8, 869-895 (1988)) and originally developed in the framework of finite elements, is checked with respect to the present high-order approach. Several tests are carried out in Cartesian geometries, successively 2D and 3D, then a comparison is performed in a cylindrical domain with two different sets of radial collocation nodes: Gauss-Lobatto nodes and Gauss-Radau points. Although quite acceptable results are obtained with the latter chain, a general decrease in efficiency is noticeable in the collocation method. This is interpreted as the consequence of two factors: the collocation formulation is not symmetric and the Fourier analysis, used as heuristic guide by CahouMt and Chabard, loses its efficiency in a non-equidistant grid, especially in a cylindrical geometry.We present an application to the study of thermosolutal convection induced by unidirectional solidification of a binary alloy. The latter grows from a Pb-30%Tl liquid phase in a cylindrical crucible corresponding to the vertical Bridgman upward configuration. We study the influence of the flow patterns on the crystal composition.
    Additional Material: 7 Ill.
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  • 59
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 445-446 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 60
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 447-448 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 61
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 11-27 
    ISSN: 0271-2091
    Keywords: finite elements ; liquid crystal ; nematic ; anisotropic ; electro rheological ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The orientation tensor L is introduced to construct a modified Leslie-Ericksen model for the viscous, incompressible flow of anisotropic suspensions (including electric field effects). This is then utilized to develop a weak variational formulation and finite element scheme for computing the flow and orientation fields. Numerical results are presented for exploratory test problems.
    Additional Material: 11 Ill.
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  • 62
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 43-66 
    ISSN: 0271-2091
    Keywords: multiple-level model ; finite element method ; open boundary condition ; tidal current analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The results of a research project to verify the newly improved multiple- level model for 3D tidal current analysis in Tokyo Bay are presented. The improved multiple-level model includes additional effects due to Coriolis force, river inflows and wind shear stresses. Furthermore, a new numerical treatment of the open boundary condition was applied which effectively eliminated the spurious reflective waves often generated by various numerical methods simulating free surface flows. The mean (time-averaged or residual) and tidal currents in Tokyo Bay were simulated as examples to demonstrate the validity and capability of the newly improved multiple-level model. A series of numerical experiments was conducted to carefully examine the tidal circulations affected by the forcing factors of Coriolis force, river inflows and wind shears, both individually and combined. The numerical results demonstrated that the effects of each forcing term are physically reasonable, with the wind shear effect being the most significant and the case including all forcing terms being in best overall agreement with the field data collected in Tokyo Bay by the Ministry of Transportation. This study has contributed not only to the verification of the newly improved multiple-level model but also to the enhancement of the accuracy of numerical simulations of three-dimensional flow in coastal waters by this model.
    Additional Material: 22 Ill.
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  • 63
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 103-120 
    ISSN: 0271-2091
    Keywords: free surface ; free boundary problem ; segregated method ; finite elements ; extrusion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An algorithm to simulate steady, viscous free surface flows is presented in this paper. A Picard-type approach wherein the flow and free surface updates are performed alternately is utilized to iterate for a solution. The procedure is intended for large-scale two- or three-dimensional problems. A surface-intrinsic co-ordinate system which facilities representation of general free surface shapes is used. Using a Galerkin finite element method (GFEM), two free surface updates, namely kinematic and normal stress updates are formulated. It is shown that the effects of surface tension, surface tension gradients and imposition of contact angles can be simulated elegantly within the framework of the GFEM. A novel feature of the updates is that the deformations are sought in a direction normal to the current iterate free surface shape, with the result that the method is ideally suited when used in conjunction with an automatic mesh generator. With the normal stress update a volume constraint can also be imposed. A segregated method is utilized to solve iteratively one degree of freedom at a time for the solution of the flow variables. As a result, the memory and disc space requirements are minimal. Sample problems in extrusion, coating and crystal growth are presented to clearly illustrate the convergence behaviour and accuracy of the algorithm.
    Additional Material: 7 Ill.
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  • 64
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 121-135 
    ISSN: 0271-2091
    Keywords: spatial marching methods ; reduced Navier-Stokes equations ; explicit methods ; Runge-Kutta method ; hypersonic flow ; supersonic flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper develops a spatial marching method for high-speed flows based on a finite volume approach. The method employs the reduced Navier- Stokes equations and a pressure splitting in the streamwise direction based on the Vigneron strategy. For marching from an upstream station to one downstream the modified five-level Runge-Kutta integration scheme due to Jameson and Schmidt is used. In addition, for shock handling and for good convergence properties the method employs a matrix form of the artificial dissipation terms, which has been shown to improve the accuracy of predictions. To achieve a fast rate of convergence, a local time-stepping concept is used. The method retains the time derivative in the governing equations and the solution at every spatial station is obtained in an iterative manner.The developed method is validated against two test cases: (a) supersonic flow past a flat plate; and (b) hypersonic flow past a compression corner involving a strong viscous-inviscid interaction. The computed wall pressure and wall heat transfer coefficients exhibit good general agreement with previous computations by other investigators and with experiments.
    Additional Material: 14 Ill.
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  • 65
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 151-173 
    ISSN: 0271-2091
    Keywords: free surface flow ; spillways ; critical flow ; finite element ; sensitivity analysis ; variable domain method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method for the computation of two-dimensional critical flows over spillways is presented. The premise of the method is that at a critical value of the discharge coefficient that free boundary has no upstream waves. For the chosen spillway geometry without a toe section this requirement is equivalent to negative curvature of the free boundary. The method consists of two levels: at the inner level the corresponding free boundary value problem is solved for a fixed value of Q and at the outer level a critical value of Q is sought by minimization of the oscillation of the free boundary. An invaluable part of the method is the sensitivity anlaysis of the finite element stiffness matrix. The correctness of the numerical results is proved by scrutinizing the convergence rate by mesh refinement. Good agreement of the computed results with experimental data is achieved.
    Additional Material: 11 Ill.
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  • 66
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 67
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    International Journal for Numerical Methods in Fluids 22 (1996), S. 937-959 
    ISSN: 0271-2091
    Keywords: incremental unknowns ; finite difference ;