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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 127-162 
    ISSN: 0271-2091
    Keywords: Least squares ; Finite element ; p-version ; Error functional ; Power-law-fluid ; Non-isothermal ; Degrees of freedom ; p-convergence ; Hierarchial ; Newton's method ; Line search ; 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 presents a p- version least squares finite element formulation (LSFEF) for two-dimensional, incompressible, non-Newtonian fluid flow under isothermal and non-isothermal conditions. The dimensionless forms of the diffential equations describing the fluid motion and heat transfer are cast into a set of first-order differential equations using non-Newtonian stresses and heat fluxes as auxiliary variables. The velocities, pressure and temperature as well as the stresses and heat fluxes are interpolated using equal-order, C0-continuous, p-version hierarchical approximation functions. The application of least squares minimization to the set of coupled first-order non-linear partial differential equations results in finding a solution vector {δ} which makes the partial derivatives of the error functional with respect to {δ} a null vector. This is accomplished by using Newton's method with a line search.The paper presents the implementation of a power-law model for the non-Newtonian Viscosity. For the non-isothermal case the fluid properties are considered to be a function of temperature. Three numerical examples (fully developed flow between parallel plates, symmetric sudden expansion and lid-driven cavity) are presented for isothermal power-law fluid flow. The Couette shear flow problem and the 4:1 symmetric sudden expansion are used to present numerical results for non-isothermal power-law fluid flow. The numerical examples demonstrate the convergence characteristics and accuracy of the formulation.
    Additional Material: 31 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994) 
    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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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 257-271 
    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
    Notes: In this paper a new, highly accurate method called PH is presented for the numerical integration of partial differential equations. The method is applied for the solution of the one-dimensional diffusion equation. Upon integrating the equation within a subdomain of space and time using the prismoidal approximation, a three-point implicit scheme is obtained with a truncation error of order O(k4, h6), where k and h represent the time and space steps respectively. The method is stable under the condition s = αk/h2 ≤ S(δ), where the function S(δ) increases as the parameter δ decreases from 1/12 to negative values. In practice the method behaves as unconditionally stable upon choosing an appropriate value for δ. A new formula is also adopted for the implementation of a Neumann boundary condition, introducing a truncation error of order O(h4). Numerical solutions are obtained incorporating Dirichlet and Neumann boundary conditions. The results prove that our method is far more accurate than any other-implicit or explicit method.
    Additional Material: 2 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 333-335 
    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 18 (1994), S. iii 
    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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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 27-42 
    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
    Notes: We are interested in solving second-order PDEs with multigrid and unstructured meshes. The multigrid strategy we present here is adapted from the generalized finite volume agglomeration multigrid algorithm we have developed recently for the solution of the Euler equations. We now focus on Poisson's equation. A strategy is defined by introducing a correction factor for the diffusive terms, and some illustrating results are given.
    Additional Material: 8 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 43-69 
    ISSN: 0271-2091
    Keywords: Least squares ; Finite element ; p-version ; Error functional ; Degrees of freedom ; p-convergence ; Newton's method ; Line search ; Navier-Stokes ; Hierarchical ; Driven cavity ; Asymmetric expansion ; 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 p-version least squares finite element formulation for non-linear problems is applied to the problem of steady, two-dimensional, incompressible fluid flow. The Navier-Stokes equations are cast as a set of first-order equations involving viscous stresses as auxiliary variables. Both the primary and auxiliary variables are interpolated using equal-order C0 continuity, p-version hierarchical approximation functions. The least squares functional (or error functional) is constructed using the system of coupled first-order non-linear partial differential equations without linearization, approximations or assumptions. The minimization of this least squares error functional results in finding a solution vector {δ} for which the partial derivative of the error functional (integrated sum of squares of the errors resulting from individual equations for the entire discretization) with respect to the nodal degrees of freedom {δ} becomes zero. This is accomplished by using Newton's method with a line search. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method.
    Additional Material: 23 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 543-544 
    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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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 605-625 
    ISSN: 0271-2091
    Keywords: Vertex-centred ; Finite volume ; Multigrid ; Navier-Stokes ; Shock detection ; Turbulence ; 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 introduces a vertex-centred finite volume method for compressible viscous flow incorporating a new shock detection procedure. The discretization is designed to be robust and accurate on the highly stretched and curved meshes necessary for resolving turbulent boundary layers around the leading edge of an aerofoil. Details of the method are described for two-dimensional problems and the natural extension of three-dimensional multiblock meshes is discussed. The shock detection procedure is used to limit the range of the shock-capturing dissipation specifically to regions containing shocks. For transonic turbulent flow this is shown to improve the boundary layer representation significantly.
    Additional Material: 15 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994) 
    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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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 669-694 
    ISSN: 0271-2091
    Keywords: Free surface ; Finite element ; Viscous 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: A new finite element procedure called the net inflow method has been developed to simulate time-dependent incompressible viscous flow including moving free surfaces and inertial effects. As a fixed mesh approach with triangular element, the net inflow method can be used to analyse the free surface flow in both regular and irregular domains. Most of the empty elements are excluded from the computational domain, which is adjusted successively to cover the entire region occupied by the liquid. The volume of liquid in a control volume is updated by integrating the net inflow of liquid during each iteration. No additional kinetic equation or material marker needs to be considered. The pressure on the free surface and in the liquid region can be solved explicitly with the continuity equation or implicitly by using the penalty function method. The radial planar free surface flow near a 2D point source and the dam-breaking problem on either a dry bed or a still liquid have been analysed and presented in this paper. The predictions agree very well with available analytical solutions, experimental measurements and/or other numerical results.
    Additional Material: 23 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 721-731 
    ISSN: 0271-2091
    Keywords: Generalized integral transform technique ; Boundary layer ; Sphere ; 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 generalized integral transform technique is applied to the boundary layer equations for flow over a sphere in their primitive variables. Even though a diffusion-based eigenvalue problem is used, the velocity profile, shear stress and separation point have been calculated with high accuracy. Low-order approximations are shown to be accurate near the surface and the predictions of the separation point is very good. Comparison with finite difference results shows the better convergence behaviour of the integral transform method.
    Additional Material: 4 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994) 
    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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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1135-1151 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Mixed formulation ; Bi-CGSTAB ; Incomplete LU ; Inner iterations ; 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 present work a new iterative method for solving the Navier-Stokes equations is designed. In a previous paper a coupled node fill-in preconditioner for iterative solution of the Navier-Stokes equations proved to increase the convergence rate considerably compared with traditional preconditioners. The further development of the present iterative method is based on the same storage scheme for the equation matrix as for the coupled node fill-in preconditioner. This storage scheme separates the velocity, the pressure and the coupling of pressure and velocity coefficients in the equation matrix. The separation storage scheme allows for an ILU factorization of both the velocity and pressure unknowns. With the inner-outer solution scheme the velocity unknowns are eliminated before the resulting equation system for the pressures is solved iteratively. After the pressure unknown has been found, the pressures are substituted into the original equation system and the velocities are also found iteratively. The behaviour of the inner-outer iterative solution algorithm is investigated in order to find optimal convergence criteria for the inner iterations and compared with the solution algorithm for the original equation system. The results show that the coupled node fill-in preconditioner of the original equation system is more efficient than the coupled node fill-in preconditioner of the reduced equation system. However, the solution technique of the reduced equation system revals properties which may be advantageous in future solution algorithms.
    Additional Material: 4 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1211-1212 
    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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  • 16
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1213-1214 
    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 19 (1994), S. 1-22 
    ISSN: 0271-2091
    Keywords: Ladle ; Two-phase flow ; Navier-Stokes ; SUPG ; Streamline diffusion ; Stabilized 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: The modelling of liquid flow in gas-stirred vessels is described. A simple two-phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas is modelled with the hypothesis of independent bubbles. The resulting PDE system is discretized with an original version of the SUPG-FEM technique which stabilizes both the convection term and equal-order interpolations for velocity and pressure, which are known to be unstable for incompressible flows. The resulting steady state discrete system is solved via pseudotemporal explicit iteration with a local time step and a preconditioning to homogenize the temporal scales for liquid and gas.
    Additional Material: 16 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 41-65 
    ISSN: 0271-2091
    Keywords: Newton's method ; Interface ; Floating zone ; Thermocapillary 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: Newton's method is applied to the finite volume approximation for the steady state heat transfer, fluid flow and unknown interfaces in a floating molten zone. The streamfunction/vorticity and temperature formulation of the Navier-Stokes and energy equations and their associated boundary conditions are written in generalized curvilinear co-ordinates and conservative law form with the Boussinesq approximation. During Newton iteration the ILU(0) preconditioned GMRES matrix solver is applied for solving the linear system, where the sparse Jacobian matrix is estimated by finite differences. Nearly quadratic convergence of the method is observed. Sample calculations are reported for sodium nitrate, a high-Prandtl-number material (Pr = 9.12). Both natural convection and thermocapillary flow as well as an overall mass balance constraint in the molten zone are considered. The effects of convection and heat input on the flow patterns, zone position and interface shapes are illustrated. After the lens effect due to the molten zone is considered, the calculated flow patterns and interface shapes are compared with the observed ones and are found to be in good agreement.
    Additional Material: 16 Ill.
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994) 
    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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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 135-152 
    ISSN: 0271-2091
    Keywords: Turbulent flow ; Swirling flow ; k-∊ model ; Control volume ; 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 control volume finite element method that uses a triangular grid has been applied for solving confined turbulent swirling flows. To treat the velocity-pressure coupling, the vorticity-streamfunction formulation has been used. For turbulence effects the k-∊ model has been adopted. Consistent with the use of wall functions in the near-wall regions, a boundary condition for the calculation of the vorticity at computational boundaries is proposed and used effectively. The discretized equations are obtained by making use of an exponential interpolation function. Its use has been beneficial in reducing numerical diffusion. Comparisons of the current predictions with available experimental and numerical data from the literature showed generally fair agreement.
    Additional Material: 17 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1-26 
    ISSN: 0271-2091
    Keywords: Axisymmetric flow ; Laminar flow ; Control-volume finite element method ; Mass-weighted skew upwind interpolation ; Flow-oriented upwind interpolation ; 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 formulation of a control-volume-based finite element method (CVFEM) for axisymmetric, two-dimensional, incompressible fluid flow and heat transfer in irregular-shaped domains is presented. The calculation domain is discretized into torus-shaped elements and control volumes. In a longitudinal cross-sectional plane, these elements are three-node triangles, and the control volumes are polygons obtained by joining the centroids of the three-node triangles to the mid-points of the sides. Two different interpolation schemes are proposed for the scalar-dependent variables in the advection terms: a flow-oriented upwind function, and a mass-weighted upwind function that guarantees that the discretized advection terms contribute positively to the coefficients in the discretized equations. In the discretization of diffusion transport terms, the dependent variables are interpolated linearly. An iterative sequential variable adjustment algorithm is used to solve the discretized equations for the velocity components, pressure and other scalar-dependent variables of interest. The capabilities of the proposed CVFEM are demonstrated by its application to four different example problems. The numerical solutions are compared with the results of independent numerical and experimental investigations. These comparisons are quite encouraging.
    Additional Material: 12 Ill.
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 123-125 
    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 18 (1994), S. 163-188 
    ISSN: 0271-2091
    Keywords: Non-linear interaction ; Hydrodynamic ; Spectral ; Finite difference ; Tidal current ; Wind-driven current ; 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 single-point model in the vertical is used to examine the coupling between tidal currents and wind-driven flows in shallow near-coastal regions. Calculations using both a linear slip and a no-slip condition at the sea bed clearly show that coupling between tidal and wind-driven currents cannot occur in a linear model with a time-independent eddy viscosity. However with a physically more realistic time-varying viscosity related to the flow field, coupling does occur, the magnitude of this non-linear interaction depending upon the change in eddy viscosity over a tidal cycle and the intensity of shear in the vertical. A point model in the vertical with flow induced by an oscillatory pressure gradient and an additional constant wind stress is used to examine the influence of viscosity parametrization and water depth upon this coupling.The solution in the vertical is accomplished using both a functional approach and a finite difference method. Some conclusions as to the relative merits of these approaches, particularly the use of a transformed grid in the case of high-shear surface and bed boundary layers, are made in the paper.
    Additional Material: 14 Ill.
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 215-226 
    ISSN: 0271-2091
    Keywords: Galerkin method ; Hermite, Lagrange and simplex finite elements ; Mixed UVP ; Continuous and discrete penalty ; Least-squares method ; Low-viscosity laminar 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 deals with a critical evaluation of various finite element models for low-viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least-squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low-viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least-squares method in conjunction with C1-continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping of C1 Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least-squares method in combination with isoparmetric Hermite elements offers a new general-purpose modelling technique which can accurately simulate all types of low-viscosity incompressible laminar flow in complex domains.
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 229-256 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Non-linear iteration ; Preconditioned 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: In this study, the discretized finite volume form of the two-dimensional, incompressible Navier-Stokes equations is solved using both a frozen coefficient and a full Newton non-linear iteration. The optimal method is a combination of these two techniques. The linearized equations are solved using a conjugate-gradient-like method (CGSTAB). Various types of preconditioning are developed. Completely general sparse matrix methods are used. Investigations are carried out to determine the effect of finite volume cell anisotropy on the preconditioner. Numerical results are given for several test problems.
    Additional Material: 9 Ill.
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  • 26
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994) 
    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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  • 27
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 693-705 
    ISSN: 0271-2091
    Keywords: Boundary conditions ; Artificial boundary ; Internal flow ; Incompressible 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: The aim of this paper is to give open boundary conditions for the incompressible Navier-Stokes equations. From a weak formulation in velocity-pressure variables, some natural boundary conditions involving the traction or pseudotraction and inertial terms are established. Numerical experiments on the flow behind a cylinder show the efficiency of these conditions, which convey properly the vortices downstream. Comparisons with other boundary conditions for the velocity and pressure are also performed.
    Additional Material: 8 Ill.
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  • 28
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 737-738 
    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
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 575-604 
    ISSN: 0271-2091
    Keywords: Radiation boundary conditions ; Open boundary conditions ; Shallow water wave equations ; Sommerfeld condition ; Klein-Gordon equation ; 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 second-order radiation boundary condition (RBC) is derived for 2D shallow water problems posed in ‘wave equation’ form and is implemented within the Galerkin finite element framework. The RBC is derived by matching the dispersion relation for the interior wave equation with an approximate solution to the exterior problem for outgoing waves. The matching is correct to second order, accounting for curvature of the wave front and the geometry. Implementation is achieved by using the RBC as an evolution equation for the normal gradient on the boundary, coupled through the natural boundary integral of the Galerkin interior problem. The formulation is easily implemented on non-straight, unstructured meshes of simple elements. Test cases show fidelity to solutions obtained on extended meshes and improvement relative to simpler first-order RBCs.
    Additional Material: 28 Ill.
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  • 30
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 647-668 
    ISSN: 0271-2091
    Keywords: Euler equations ; Finite element method ; Implicit scheme ; Unsteady flow ; Transonic 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: An implicit finite element method is presented for the solution of steady and unsteady inviscid compressible flows on triangular meshes under transonic conditions. The method involves a first-order time-stepping scheme with a finite element discretization that reduces to central differencing on a rectangular mesh. On a solid wall the slip condition is prescribed and the pressure is obtained from an approximation of the normal momentum equation. With this solver no artificial viscosity is added to ensure the success of the calculation. Numerical examples are given for steady and unsteady cases.
    Additional Material: 12 Ill.
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  • 31
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 687-692 
    ISSN: 0271-2091
    Keywords: Open boundary conditions ; Flow stability ; 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 consider uniform flow of a Newtonian fluid trasverse to a domain bounded by parallel planes. We investigate the possibility of introducing instabilities in this flow by the choice of inflow and outflow conditions. Some instabilities of this kind are found.
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  • 32
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 827-847 
    ISSN: 0271-2091
    Keywords: TVD ; Unstructured mesh algorithms ; Euler equations ; Hypersonic 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: The Galerkin finite element method is used as the basis for the construction of schemes for the solution of the two-dimensional compressible Euler equations on unstructured triangular grids. The use of a side-based data structure readily allows for the construction of a local (structured) stencil and the incorporation of a high-resolution shock-capturing method formulated within the TVD concept. The essential features of the finite element side-based scheme and the ID TVD approach are described and their numerical implementation is discussed. The choice of limiters and the support for their computation are analysed and the solutions of some inviscid flows, obtained by advancing explicitly in time, are presented.
    Additional Material: 18 Ill.
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  • 33
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 869-888 
    ISSN: 0271-2091
    Keywords: k-∊ model ; Two-layer model ; Low-Reynolds number model ; Wall function 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 fully elliptic Reynolds-averaged Navier-Stokes equations have been used together with Lam and Bremhorst's low-Reynolds-number model, Chen and Patel's two-layer model and a two-point wall function method incorporated into the standard k-∊ model to predict channel flows and a backward-facig step flow. These flows enable the evaluation of the performance of different near-wall treatments in flows involving streamwise and normal pressure gradients, flows with separation and flows with non-equilibrium turbulence characteristics. Direct numerical simulation (DNS) of a channel flow with Re =3200 further provides the detailed budgets of each modelling term of the k and ∊-transport equations. Comparison of model results with DNS data to evaluate the performance of each modelling term is also made in the present study. It is concluded that the low-Reynolds-number model has wider applicability and performs better than the two-layer model and wall function approaches. Comparison with DNS data further shows that large discrepancies exist between the DNS budgets and the modelled production and destruction terms of the ∊ equation. However, for simple channel flow the discrepancies are similar in magnitude but opposite in sign, so they are cancelled by each other. This may explain why, even when employing such an inaccurately modelled ∊-equation, one can still predict satisfactorily some simple turbulent flows.
    Additional Material: 14 Ill.
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  • 34
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 959-960 
    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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  • 35
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 961-979 
    ISSN: 0271-2091
    Keywords: Confined flow ; Swirling flow ; 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: The bifurcation of confined swirling flows was numerically investigated by employing both the k-∊ and algebraic stress turbulence models. Depending upon the branch solution examined, dual flow patterns were predicted at certain swirl levels. In the lower-branch solution which is obtained by gradually increasing the swirl level from a low-swirl flow, the flow changes with increasing swirl number from the low-swirl flow pattern to a high-swirl flow pattern. In the upper-branch solution which is acquired by gradually decreasing the swirl level from a high-swirl flow, on the other hand, the flow can maintain itself in the high-swirl flow pattern at the swirl levels where it exhibits the low-swirl flow pattern in the lower branch. The bifurcation of confined swirling flows was predicted with either the k-∊ model or the algebraic stress model being employed. Both the k-∊ and algebraic stress models result in comparable and sufficiently good predictions for confined swirling flows if high-order numerical schemes are used. The reported poor performance of the k-∊ model was clarified to be mainly attributable to the occurrence of the bifurcation and the use of low-order numerical schemes.
    Additional Material: 12 Ill.
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  • 36
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 997-1012 
    ISSN: 0271-2091
    Keywords: Advection ; Method of characteristics ; Finite difference ; Flux limiter ; 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 use of the highest-order ((N - 1)th-order) Lagrangian interpolation Polynomial for the approximation of the exact solution in the backward characteristics scheme with N nodes is inefficient owing to the excessive number of terms in the polynomial. New schemes based on a combination of lower-order polynomials to approximate the exact solution are developed, with the relative weighting of the polynomials determined by Fourier mode analysis. With the addition of a flux limiter and a modified discriminator, the resulting schemes are oscillation-free, highly accurate, efficient and more cost-effective as compared with those schemes using the highest-order Lagrangian polynomial.
    Additional Material: 6 Ill.
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  • 37
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 889-903 
    ISSN: 0271-2091
    Keywords: SIMPLE-like algorithm ; Average pressure correction ; Paper filter ; Turbulent flow ; Sampler ; 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 control volume, finite difference method and the k-∊ tubulence model are employed in a numerical simulation of the turbulent fluid flow both outside and inside a blunt cylindrical sampler which houses a paper filter in its chamber. The presence of a paper filter, which has a very large resistance, results in a large pressure drop across the filter and this causes difficulties in making the SIMPLE or the SIMPLEC scheme converge. In order to improve the rate of convergence of the SIMPLE-like algorithm when the resistance of the filter is very large, an average pressure correction formula is proposed. Based on global mass conservation, a line average pressure correction for the paper filter is derived using a modified Darcy law for a porous medium. A combination of this formula and the SIMPLE-like algorithm can rapidly build up the pressure drop across the filter and hence dramatically improve the rate of convergence of the iterative scheme. Comparisons of the convergence histories and the numerical results for the fluid flow when using SIMPLE and SIMPLEC with the average pressure correction method show that the average pressure correction method for dealing with the paper filter significantly accelerates the rate of convergence of the iterative scheme.
    Additional Material: 12 Ill.
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  • 38
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 905-938 
    ISSN: 0271-2091
    Keywords: Dynamic vorticity condition ; Theoretical 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 dynamic boundary conditions for vorticity, derived from the incompressible Navier-Stokes equations, are examined from both theoretical and computational points of view. It is found that these conditions can be either local (Neumann type) or global (Dirichlet type), both containing coupling with the boundary pressure, which is the main difficulty in applying vorticity-based methods. An integral formulation is presented to analyse the structure of vorticity and pressure solutions, especially the strength of the coupling. We find that for high-Reynolds-number flows the coupling is weak and, if necessary, can be effectively bypassed by simple iteration. In fact, even a fully decoupled approximation is well applicable for most Reynolds numbers of practical interest. The fractional step method turns out to be especially appropriate for implementing the decoupled approximation. Both integral and finite difference methods are tested for some simple cases with known exact solutions. In the integral approach smoothed heat kernels are used to increase the accuracy of numerical quadrature. For the more complicated problem of impulsively started flow over a circular cylinder at Re = 9500 the finite difference method is used. The results are compared against numerical solutions and fine experiments with good agreement. These numerical experiments confirm our thoeretical analysis and show the advantages of the dynamic condition in computing high-Reynolds-number flows.
    Additional Material: 14 Ill.
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  • 39
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 939-956 
    ISSN: 0271-2091
    Keywords: Turbulence models ; Confined jets ; Recirculation ; 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 numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-∊ model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-∊ model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reatachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite volume procedure. Numerical credibility of the solutions is ensured by using second-order-accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-∊ model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-∊ model in capturing the essential flow features, while the RNG-based K-∊ model does not seem to give improvements over the standard K-∊ model under the flow conditions considered.
    Additional Material: 12 Ill.
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  • 40
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    International Journal for Numerical Methods in Fluids 19 (1994) 
    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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  • 41
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 981-995 
    ISSN: 0271-2091
    Keywords: Pressure-based method ; All-speed ; Blast wave ; Two-phase flow ; Combustion instability ; 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 improved pressure-based method has been applied to predict the two-dimensional instability analysis of liquid-fuelled rocket engines. This method is non-iterative for transient flow calculations and applicable to all-speed flows. Validation cases include the shock-tube problem, the blast flow field and unsteady spraycombusting flows. Computations for the combustion instability analysis were carried out for various combustion parameters such as spray initial conditions and combustor geometries. Unsteady behaviours of the stable and unstable spray flame fields and effects of acoustic oscillations on the fuel droplet vaporization and combustion process are studied in detail. The present numerical model successfully demonstrates the capability of predicting combustion instability as well as fast transient compressible flows at all speeds.
    Additional Material: 14 Ill.
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  • 42
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 1051-1053 
    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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  • 43
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    International Journal for Numerical Methods in Fluids 19 (1994), S. i 
    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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  • 44
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 1055-1081 
    ISSN: 0271-2091
    Keywords: Multiphase porous media flow ; Primary variable selection ; Horizontal wells ; 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 simulation of steam flush for clean-up of non-aqueous phase liquid (NAPL) contaminated groundwater sites involves solution of the multiphase, multicomponent subsurface flow equations. This paper describes techniques for discretizing problems with horizontal wells in a three-dimensiontetrahedral mesh. The effectiveness of non-linear flux limiters for reducing numerical dispersion is discussed. Primary variable selection and thermodynamic state transition rules will also be compared. Some example results for several steam flush scenarios will be presented.
    Additional Material: 21 Ill.
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  • 45
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 1137-1138 
    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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  • 46
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 89-103 
    ISSN: 0271-2091
    Keywords: Air entrainment ; Pressure surges ; Wave speed ; Pumping installations ; 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 pumping installations such as sewage pumping stations, where gas content and air entrainment exist, the computation of fluid pressure transients in pipelines becomes grossly inaccurate when a constant wave speed is assumed. An accurate numerical model with gas release and absorption has been developed in this paper and used to compute the fluid pressure transients in the pumping mains of selected pumping installations. Free and dissolved gases in the transported fluid and cavitation at vapour pressure are also modelled. When compared with the gas-free case, computations show that entrained, entrapped or released gases amplify the positive pressure peak, increase surge damping and produce asymmetric pressure surges. While the upsurge with air entrainment in the pipelines was considerably amplified, the downsurge was only marginally reduced. The computed results show good agreement with the data available.
    Additional Material: 12 Ill.
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  • 47
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 363-364 
    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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  • 48
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 395-413 
    ISSN: 0271-2091
    Keywords: Euler implicit scheme ; Pseudocompressibility ; Moving grid system ; Free surface fitting ; Baldwin-Lomax 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 Navier-Stokes equation solver is developed for computing free surface wave and viscous flow around an arbitrary body, in which a free surface model is introduced into the pseudocompressibility solution. The governing equations are classified in a vectorial form, with primitive variables, and a block diagonal system is generated by the discretization of an implicit factorization method. A moving grid system fitted to both the free surface and body surface is generated by an effective cubic spline fitting technique. Two zero-equation turbulence models, namely the Cebeci-Smith model and the Baldwin-Lomax model, are used for turbulent calculations. Numerical simulations are carried out for the free surface viscous flows generated by a submerged hydrofoil and a ship model. Computed results are in reasonable agreement with measurements.
    Additional Material: 14 Ill.
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  • 49
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 459-462 
    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 19 (1994), S. 439-455 
    ISSN: 0271-2091
    Keywords: Incompressible Navier-Stokes ; Newton's method ; 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: An inexact Newton method is used to solve the steady, incompressible Navier-Stokes and energy equation. Finite volume differencing is employed on a staggered grid using the power law scheme of Patankar. Natural convection in an enclosed cavity is studied as the model problem. Two conjugate-gradient -like algorithms based upon the Lanczos biorthogonalization procedure are used to solve the linear systems arising on each Newton iteration. The first conjugate-gradient-like algorithm is the transpose-free quasi-minimal residual algorithm (TFQMR) and the second is the conjugate gradients squared algorithm (CGS). Incomplete lower-upper (ILU) factorization of the Jacobian matrix is used as a right preconditioner. The performance of the Newton- TFQMR algorithm is studied with regard to different choices for the TFQMR convergence criteria and the amount of fill-in allowed in the ILU factorization. Performance data are compared with results using the Newton-CGS algorithm and previous results using LINPACK banded Gaussian elimination (direct-Newton). The inexact Newton algorithms were found to be CPU competetive with the direct-Newton algorithm for the model problem considered. Among the inexact Newton algorithms, Newton-CGS outperformed Newton- TFQMR with regard to CPU time but was less robust because of the sometimes erratic CGS convergence behaviour.
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  • 51
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    International Journal for Numerical Methods in Fluids 19 (1994) 
    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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  • 52
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    International Journal for Numerical Methods in Fluids 18 (1994), S. 361-383 
    ISSN: 0271-2091
    Keywords: Boundary-fitted co-ordinates ; Stratified flow ; Hydrostatic pressure ; 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 stratified three-dimensional models the use of a boundary-fitted vertical co-ordinate is known to produce errors in the horizontal pressure gradient calculation near steep topography. The error is due to the splitting of the horizontal pressure gradient term in each of the momentum equations into two parts and the subsequent incomplete cancellation of the truncation errors of those parts. In order to minimize these pressure gradient errors, a fourth-order-accurate pressure gradient calculation has been implemented and installed in SPEM, a three-dimensional primitive equation ocean model. The stability and accuracy of the new scheme are compared with those of the original second-order-accurate model in a series of calculations of unforced flow in the vicinity of an isolated seamount. The new scheme is shown to have much smaller pressure gradient errors over a wide range of parameter space as well as a greater parametric domain of numerical stability.
    Additional Material: 14 Ill.
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  • 53
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    International Journal for Numerical Methods in Fluids 18 (1994) 
    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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  • 54
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    International Journal for Numerical Methods in Fluids 18 (1994), S. 747-760 
    ISSN: 0271-2091
    Keywords: Computer-aided design ; Adaptive methods ; Panel methods ; Computational fluid dynamics ; 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 work outlined below presents simple but effective adaptive meshing algorithms for boundary integral methods modelling inviscid flows (panel method) using the IGES standard for describing geometry. By using certain IGES entities in describing the boundary, CAD-derived geometry may be used such that the geometric integrity of the boundary is maintained after an adaptive redistribution of the mesh. Three types of error estimators are tested and all are shown to produce a more accurate representation of the flow phenomena for the same number of panels as compared with a uniform mesh distribution.
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  • 55
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 269-270 
    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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  • 56
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 275-294 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Fully-coupled solution ; Iterative solvers ; Finite-element methods ; Parallel algorithm ; Block diagonal preconditioning ; CFD ; 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 presents the parallelization aspects of a solution method for the fully coupled 3D compressible Navier-Stokes equations. The algorithmic thrust of the approach, embedded in a finite element code NS3D, is the linearization of the governing equations through Newton methods, followed by a fully coupled solution of velocities and pressure at each non-linear iteration by preconditioned conjugate gradient-like iterative algorithms. For the matrix assembly, as well as for the linear equation solver, efficient coarse-grain parallel schemes have been developed for shared memory machines, as well as for networks of workstations, with a moderate number of processors. The parallel iterative schemes, in particular, circumvent some of the difficulties associated with domain decomposition methods, such as geometry bookkeeping and the sometimes drastic convergence slow-down of partitioned non-linear problems.
    Additional Material: 15 Ill.
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  • 57
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 321-342 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Free surface flow ; Finite difference ; Wave resistance ; Frictional resistance ; Adaptive mesh ; 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 present here a numerical method for solving the free surface flow around a ship at forward speed in calm water. The fluid is assumed to be Newtonian and the Reynolds-averaged Navier-Stokes equations are solved by a finite difference method. Modelization of turbulence is achieved by the algebraic model proposed by Baldwin and Lomax. Fully non-linear free surface conditions are satisfied in the model and a method to avoid the incompatibility between free surface conditions and no-slip conditions at the waterline is proposed. Numerical results obtained for a Wigley hull are compared with experimental results.
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  • 58
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    International Journal for Numerical Methods in Fluids 19 (1994), S. 365-367 
    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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  • 59
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    International Journal for Numerical Methods in Fluids 18 (1994), S. 1185-1209 
    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
    Notes: Two approaches which employ the finite element method to solve for large-scale, coupled, incompressible flows through adjacent porous and open domains are developed and evaluated in a model for the spontaneous ignition of coal stockpiles. Both formulations employ the Navier-Stokes equations do describe flow in the open region; two different descriptions, Darcy's law and the Brinkman equation, are employed to model flows within the porous region. The formulation which uses Darcy's law employs the Beavers-Joseph slip condition and a novel implementation of the interfacial conditions. The other approach invokes the Brinkman equation: this considerably simplifies the implementation of matching conditions at the interface between the porous and open fluid domains, but also results in velocity boundary layers in the porous region adjacent to this interface which can be difficult to resolve numerically. A direct comparison of model results shows that the Darcy-slip formulation produces solutions which are more accurate and more economical to compute than those obtained using the Brinkman formulation.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 60
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. iii 
    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 19 (1994), S. 67-83 
    ISSN: 0271-2091
    Keywords: Mixed finite elements ; Navier-Stokes ; Conjugate gradients ; 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 linear system arising from a Lagrange-Galerkin mixed finite element approximation of the Navier-Stokes and continuity equations is symmetric indefinite and has the same block structure as a system arising from a mixed finite element discretization of a Stokes problem. This paper considers the iterative solution of such a system, comparing the performance of the one-level preconditioned conjugate residual method for indefinite matrices with that of a more traditional two-level pressure correction approach. Asymptotic estimates for the amount of work involved in each method are given together with the results of related numerical experiments.
    Additional Material: 6 Ill.
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  • 62
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 493-512 
    ISSN: 0271-2091
    Keywords: Developing flow ; Eccentric annular ducts ; 3 + D Navier-Stokes solution ; 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 control-volume-based solution of the complete set of Navier-Stokes equations for the laminar, three-dimensional developing flow in straight, eccentric, cylindrical annular ducts is described. Numerical results for velocity and pressure development, pressure defect and entrance lengths are presented for a wide range of duct parameters, i.e. relative eccentricity ∊ and radius ratio γ. The present results match very well with earlier numerical solutions for the limiting cases of developing flow in concentric ducts and fully developed flow in eccentric ducts. Comparison with earlier approximate results for developing flow in eccentric ducts indicates that the approximate model predicts the velocity and pressure development with an error of about 10%. However, the development length predicted by the approximate model is grossly in error. The pressure defect and development length in eccentric ducts are very high compared with their counterparts in concentric ducts. The pressure defect, development length and maximum velocity increase with the radius ratio for eccentric ducts, while the reverse is true for concentric ducts. Also, the apparent friction factor decreases as the eccentricity increases.
    Additional Material: 15 Ill.
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  • 63
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 551-554 
    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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  • 64
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 153-176 
    ISSN: 0271-2091
    Keywords: Free surface fluid flow ; Impact ; Viscous ; Incompressible ; Two-dimensional ; Finite difference simulation ; Marker and cell ; 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: Deficiencies associated with the simulation of impacts of fluid free surfaces with solid boundaries by use of marker-and-cell methods are identified and addressed. New procedures are introduced that affect the movement of markers in cells adjacent to a solid boundary, the flags of the cells that comprise a solid boundary and the pressure boundary condition for a cell in which impact occurs. Combined with fundamental changes in the sequence of steps in the computational cycle, these new procedures allow the intentional treatment of impact. As a result, improved estimates are obtained of the pressure associated with the cells adjacent to a boundary along which impact occurs. Consequently, more appropriate adjustments are made of the tentative internal velocities associated with such cells. In addition, a special procedure is presented for the adjustment of the tentative internal velocity between two surface cells. Finally, a new cell type termed a corner cell is defined and a procedure for its treatment is presented. Numerical examples are included to illustrate the previous deficiencies associated with the simulation of impact as well as the effectiveness of the new methods presented in this paper. Validation of the new methods is achieved by comparison with experimental results for spillage over a containment dike.
    Additional Material: 15 Ill.
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  • 65
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 415-432 
    ISSN: 0271-2091
    Keywords: Aerodynamics ; Aerodynamic design ; Inverse problems ; Body shaping ; 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 axial singularity inverse method for designing bodies of revolution has been improved by using higher-order doublet elements. The performance of the method for various element orders and other solution parameters is presented in detail. The results indicate that the method is generally more robust, less sensitive to insets and has a better-conditioned coefficient matrix compared with the source method of the same order. The condition number of the matrix is shown to increase with the thickness of the body, the order of the method, the number of elements and the degree of stretching of the node distribution. In general, good performance is attained for most bodies even with ƒr as low as 2 by using 10-12 second-order doublet elements with insets greater than 0.02L from rounded ends. Increasing the insets to 0.06L appears to improve the accuracy of the method for most bodies but slows its convergence.
    Additional Material: 9 Ill.