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  • Engineering General  (3,144)
  • 1990-1994  (3,144)
  • 1950-1954
  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 889-905 
    ISSN: 0271-2091
    Keywords: Computational fluid dynamics ; Parallel computing ; Parallel processing ; Domain decomposition ; 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 concurrent algorithm for the solution óf the Navier-Stokes equations expressed in curvilinear co-ordinates has been developed for execution on a distributed memory parallel computer. This algorithm offers the ultimate promise of near-supercomputer performance on relatively low-cost parallel computers. The new algorithm is based on an existing serial pressure-correction-based algorithm, and uses domain decomposition to partition the problem onto the processors. The algorithm is demonstrated on an Intel iPSC for a complicated two-dimensional laminar flow problem, for various grid sizes and numbers of processors. Initial results based on straightforward domain decomposition showed that the speed-up per iteration approached 100% parallel efficiency as the grid size was increased, but that the convergence rate of the algorithm deteriorated relative to the original serial algorithm as the number of processors was increased, limiting the speed-up achieved. This degradation in convergence rate was traced to a poorer solution of the pressure correction equation in the concurrent procedure. The addition of a global block correction procedure, implemented via efficient global communications routines, remedied this problem, making the convergence rate of the concurrent procedure equivalent to the serial algorithm. The maximum speed-up achieved with the revised concurrent algorithm was a factor of 12·3 with 16 processors, representing a parallel efficiency of 77%.
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  • 2
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 925-945 
    ISSN: 0271-2091
    Keywords: Bi-conjugate gradient ; Conjugate gradient ; Conjugate gradient squared ; Finite elements ; Flow simulation ; Preconditioning ; Vector processor ; Frontal solver ; Navier-Stokes ; Boussinesq approximation Newton method ; Picard iteration ; Galerkin method ; Petrov-Galerkin ; 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 series of numerical experiments on the Cray XMP/48 and on the Cray 2 investigate the robustness and economy of direct and unsymmetric conjugate gradient (CG) type methods for the solution of matrix systems arising from a 3D FEM discretization of fluid flow problems. Computations on a Boussinesq flow model problem with either ILU preconditioned or unpreconditioned unsymmetric CG methods are presented. Such experiments seem to indicate that the unpreconditioned BICG method is robust for moderately non-linear incompressible Navier-Stokes FEM discretizations and that the ILU preconditioned BICG method is very robust and more economic than an unsymmetric frontal solver when the generous memory of the Cray 2 is exploited to store both the matrix and its preconditioner. We cover some of the programming aspects of direct and iterative methods on a supercomputer and find that direct methods have advantages: the crucial CPU-consuming area of code is compact but overwhelming, and its percentage of total CPU usage is independent of the spectral properties of the matrix involved. An optimal implementation of the unsymmetric CG method is more difficult because its work is related to the spectral distribution of the matrix considered and because there is no single portion of the code that overwhelmingly dominates the CPU usuage.
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  • 3
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 179-197 
    ISSN: 0271-2091
    Keywords: Inverse problem ; Blade design ; Turbomachines ; Finite elements ; Aerodynamic design ; Subsonic 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 mixed spectral finite element scheme for the implementation of a design method for turbomachinery blading in three-dimensional subcritical compressible flow is presented. The method gives the detailed blade shape that would produce a prescribed tangential mean swirl schedule, given the hub and shroud profiles, the number of blades and their stacking position. After a presentation of the mathematical formulation of the design theory, the current numerical approach is described. It is then applied to the design of blading for radial inflow turbine impellers in three-dimensional flow.
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  • 4
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 199-211 
    ISSN: 0271-2091
    Keywords: Finite difference ; Natural convection ; Enclosure flow ; Non-orthogonal co-ordinates ; 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 control-volume-based finite difference method in non-orthogonal curvilinear coordinates on a local basis in which the vectors and tensors are all based on the general curvilinear coordinates for buoyant flow calculations in arbitrary three-dimensional geometries. The governing equations are transformed from Cartesian co-ordinates into generalized curvilinear co-ordinates. After integrating the set of equations for the control volumes, the finite difference equations are then formulated by a proper treatment of the heat flux and stress tensors and by incorporating the QUICK scheme for the convective terms. The solution procedure then follows the one for three-dimensional Cartesian co-ordinates.Examples are given in problems of natural convection in such three-dimensional enclosures as parallelepiped enclosures and horizontal closed cylinders with differentially heated ends. In the latter case, important applications have been found in crystal growth by means of chemical vapour deposition in a cylindrical ampoule, in which uniform heat fluxes along the two ends are required in order to produce high-quality crystals. Special attention is given to the insertion of baffles in the cylinder to improve the recirculating flow patterns near the two ends.
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  • 5
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 603-606 
    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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  • 6
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 623-636 
    ISSN: 0271-2091
    Keywords: Least-squares method ; Optimal control problem ; Conjugate gradient ; Advection-diffusion equation ; Perturbation series ; 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 least-squares formulation associated with a conjugate gradient algorithm is proposed for the solution of transport problems. In this procedure the advection-diffusion equation is first discretized in time using an implicit scheme. At each time step the resulting partial differential equation is replaced by an optimal control problem. This minimization problem involves the minimization of a functional defined via a state equation. This functional is chosen in order to force the numerical solution of the advection-diffusion equation to be equal to the hyperbolic advective part of this equation. The effectiveness of the method is shown through a one-dimensional example involving advective and diffusive transport. No oscillation and high accuracy have been obtained for the entire range of Peclet numbers with a Courant number well in excess of unity.
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  • 7
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 753-769 
    ISSN: 0271-2091
    Keywords: Moving finite element method ; Population balance equation ; Particle growth ; First-order hyperbolic partial differential 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 moving finite element algorithm has been compared against the upwind-differencing and Smolarkiewicz methods for the population balance equation of multicomponent particle growth processes. Analytical solutions and an error function have been used to test the numerical methods. The moving finite elements technique is much more accurate than other methods for a wide range of parameters. Since this method uses moving grids, it is able to model very narrow particle size distributions. It is also shown that the method can be extended to solve condensational growth problems which include particle curvature and non-continuum mass transfer effects.
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  • 8
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 429-442 
    ISSN: 0271-2091
    Keywords: Uzawa algorithm ; Preconditioning ; Incomplete factorization ; Three-dimensional ; Fluid 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 iterative algorithm for the solution of the three-dimensional Navier-Stokes equations by the finite element method is presented. This algorithm is based on a combination of the Uzawa and the Arrow-Hurwicz algorithms and uses a preconditioning technique to enhance convergence. Numerical tests are presented for the cubic cavity problem with two elements, namely the linear brick Q1-P0 and the enriched linear brick Q1+ - P1. It is shown that the proposed methodology is optimal with the enriched element and that the CPU time varies as NEQ1·44, where NEQ is the number of equations.
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  • 9
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 713-721 
    ISSN: 0271-2091
    Keywords: Boundary node correction ; Pressure smoothing ; Finite element method ; Superconvergence ; Posterior error analysis ; Multiple mesh extrapolation ; 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: Convergence improvement and superconvergence behaviour, obtained by the simple boundary node correction (BNC) procedure for certain stress-like variables of smoothed FEM solutions, are reported in this paper. The effectiveness of BNC is shown through three examples of steady flow problems, and a posterior error analysis based on the multiple-mesh extrapolation technique has been used for estimating the convergence rates.
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  • 10
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 729-740 
    ISSN: 0271-2091
    Keywords: Delta wing ; Leading edge separation ; Free vortex ; Iteration Sideslip ; Rolling moment ; Dihedral ; 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 flow over a flat plate delta wing at incidence and in sideslip is studied using vortex lattice models based on streamwise penelling. For the attached flow problem the effect of sideslip is simulated by modifying the standard vortex lattice model for zero sideslip by aligning the trailing vortices aft of the wing along the resultant flow direction. For the separated flow problem a non-linear vortex lattice model is developed for both zero and non-zero sideslip angles in which the shape and position of the leading edge separation vortices are calculated by an iterative procedure starting from an assumed initial shape. The theoretical values are compared with available theoretical and experimental results.
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  • 11
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    International Journal for Numerical Methods in Fluids 10 (1990), S. 849-853 
    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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  • 12
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 881-891 
    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: There are two methods of using the magnetic vector potential for three-dimensional eddy current calculations. The first method uses the continuous magnetic vector potential which accompanies a scalar potential and has the advantage that no cutting is necessary for the multiply connected region problem. The second method uses the discontinuous magnetic vector potential which accompanies no scalar potential and has the disadvantage that cutting is necessary for the multiply connected region problem. In this paper a formulation using the continuous magnetic vector potential and accompanying scalar potential is given, together with computed results for three three-dimensional multiply connected eddy current problems.
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  • 13
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990) 
    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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  • 14
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 953-967 
    ISSN: 0271-2091
    Keywords: Finite element ; Navier-Stokes ; Outflow boundary conditions ; Backward-facing step ; 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 solution for steady incompressible flow over a two-dimensional backward-facing step is developed using a Galerkin-based finite element method. The Reynolds number for the simulations is 800. Computations are performed on an extended channel length to minimize the effect of the outflow boundary on the upstream recirculation zones. A thorough mesh refinement study is performed to validate the results. Extensive profile data at several channel locations are provided to allow future testing and evaluation of outflow boundary conditions.
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  • 15
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 1039-1042 
    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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  • 16
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 209-226 
    ISSN: 0271-2091
    Keywords: Finite elements ; Atmospheric flow ; Petrov-Galerkin ; Staggered grids ; Hybrid 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: Different finite element schemes are investigated with respect to their application in numerical weather prediction. Different methods of staggering of variables are considered. The tests concern the accuracy of a Rossby wave prediction and the generation of noise in a geostrophic adjustment process. Theoretical results concerning the noise level of different schemes are confirmed by computations with a one-dimensional model. Favourable results were obtained by hybrid schemes, using different Galerkin treatments for different terms of the dynamic equations.
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  • 17
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 59-80 
    ISSN: 0271-2091
    Keywords: Thermocapillary flow ; Natural convection ; Melt/solid interface ; Grashof number ; Marangoni number ; Prandtl number ; 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 vertical melt column set up between an upper heating rod and a lower sample rod, i.e. the so-called halfzone system, is a convenient experimental tool for studying convection in the melt in floating-zone crystal growth. In order to help understand the convection observed in the melt column, a computer model has been developed to describe steady state, axisymmetrical thermocapillary flow and natural convection in the melt. The governing equations and boundary conditions are expressed in general non-orthogonal curvilinear co-ordinates in order to accurately treat the unknown melt/solid interface as well as all other physical boundaries in the system. The effects of key dimensionless variables on the following items are discussed: (1)convection and temperature distribution in the melt; (2) the shape of the melt/solid interface; (3) the height of the melt column. These dimensionless variables are the Grashof, Marangoni and Prandtl numbers.
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  • 18
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    International Journal for Numerical Methods in Fluids 12 (1991) 
    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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  • 19
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 143-160 
    ISSN: 0271-2091
    Keywords: Adaptive grid computation ; Natural convection ; Navier-Stokes flow ; Curvilinear coordinates ; 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 model has been developed to compute the thermofluid transport within a discharge arctube. The model has proved very useful for guiding the choice of design parameters to optimize the lamp performance. However, uncertainties exist with respect to quantitative aspects of the physical model, especially those related to radiation heat transfer. In the present work a grid refinement procedure and an adaptive grid method are used to improve the quantitative accuracy of the model and to help improve the physical modelling. The adaptive grid method, based on the multiple one-dimensional equidistribution concept, can responsively redistribute the grids to optimize the grid resolutions. Adaptive grid solutions modify the predicted maximum gas temperature, the buoyancy-induced convection strength, the location of the high-temperature core, and the wall temperature profiles. The adaptive grid solutions show more consistent trends when compared to the measurements. On the basis of the quantitatively more definite information, adjustments can be made with regard to the uncertainties of the physical model.
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  • 20
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    International Journal for Numerical Methods in Fluids 11 (1990) 
    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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  • 21
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 405-426 
    ISSN: 0271-2091
    Keywords: TVD ; TVB ; ENO ; Finite element ; Euler 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: A class of shock-capturing Petrov-Galerkin finite element methods that use high-order non-oscillatory interpolations is presented for the one-dimensional compressible Euler equations. Modified eigenvalues which employ total variation diminishing (TVD), total variation bounded (TVB) and essentially non-oscillatory (ENO) mechanisms are introduced into the weighting functions. A one-pass Euler explicit transient algorithm with lumped mass matrix is used to integrate the equations. Numerical experiments with Burgers' equation, the Riemann problem and the two-blast-wave interaction problem are presented. Results indicate that accurate solutions in smooth regions and sharp and non-oscillatory solutions at discontinuities are obtainable even for strong shocks.
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  • 22
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 427-444 
    ISSN: 0271-2091
    Keywords: Fourier analysis ; Eulerian-Lagrangian ; Least squares ; Transport ; 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 Fourier analysis was performed in order to study the numerical characteristics of the effective Eulerian-Lagrangian least squares collocation (ELLESCO) method. As applied to the transport equation, ELLESCO requires a C1-continuous trial space and has two degrees of freedom per node. Two coupled discrete equations are generated for a typical interior node for a one-dimensional problem. Each degree of freedom is expanded separately in a Fourier series and is substituted into the discrete equations to form a homogeneous matrix equation. The required singularity of the system matrix leads to a ‘physical’ amplification factor that characterizes the numerical propagation of the initial conditions and a ‘computational’ one that can affect stability.Unconditional stability for time-stepping weights greater than or equal to 0-5 is demonstrated. With advection only, ELLESCO accurately propagates spatial wavelengths down to 2Δx. As the dimensionless dispersion number becomes large, implicit formulations accurately propagate the phase, but the higher-wave-number components are underdamped. At large dispersion numbers, phase errors combined with underdamping cause oscillations in Crank-Nicolson solutions. These effects lead to limits on the temporal discretization when dispersion is present. Increases in the number of collocation points per element improve the spectral behaviour of ELLESCO.
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  • 23
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 515-539 
    ISSN: 0271-2091
    Keywords: Vorticity-streamfunction ; Unsteady 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: A review of our solution techniques for the vorticity-streamfunction formulation of two-dimensional incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite element formulations for multiply connected domains is emphasized. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov-Galerkin method is used. The adaptive implicit-explicit and grouped element-by-element solution strategies are employed to maximize the computational efficiency. The solutions obtained in all test cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable and efficient.
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  • 24
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 507-533 
    ISSN: 0271-2091
    Keywords: Finite elements ; Hydrodynamics ; Three-dimensional hydrodynamics ; Non-linear hydrodynamics ; Tidal hydrodynamics ; 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 development and application of a non-linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi-implicit time-stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field-scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system.
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  • 25
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 867-880 
    ISSN: 0271-2091
    Keywords: Adaptive implicit-explicit ; Grouped element-by-element ; 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: Iterative versions of the adaptive implicit-explicit method are presented for the finite element computation of flow problems with particular reference to incompressible flows and advection-diffusion problems. The iterative techniques employed are the grouped element-by-element and generalized minimum residual methods.
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  • 26
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 849-865 
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-stokes ; Rotating cylinders ; Viscous dissipation ; 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 computational study of viscous flow between two eccentrically rotating cylinders is presented in which the effect of viscous dissipation is taken into account. The space discretization is based on piecewise linear finite elements with velocity stabilization, while the method of characteristics is used for time integration. Numerical results illustrate the efficiency of the adopted approach.
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  • 27
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 893-906 
    ISSN: 0271-2091
    Keywords: Adaptive ; Characteristic ; Flux-corrected Transport ; Petrov-Galerkin ; 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: Three adaptive finite element methods based on equidistribution, elliptic grid generation and hybrid techniques are used to study a system of reaction-diffusion equations. It is shown that these techniques must employ sub-equidistributing meshes in order to avoid ill-conditioned matrices and ensure the convergence of the Newton method. It is also shown that elliptic grid generation methods require much longer computer times than hybrid and static rezoning procedures. The paper also includes characteristic, Petrov-Galerkin and flux-corrected transport algorithms which are used to study a linear convection-reaction-diffusion equation that has an analytical solution. The flux-corrected transport technique yields monotonic solutions in good agreement with the analytical solution, whereas the Petrov-Galerkin method with quadratic upstream-weighted functions results in very diffused temperature profiles. The characteristic finite element method which uses a Lagrangian-Eulerian formulation overpredicts the flame front location and exhibits overshoots and undershoots near the temperature discontinuity. These overshoots and undershoots are due to the interpolation of the results of the Lagrangian operator onto the fixed Eulerian grid used to solve the reaction-diffusion operator, and indicate that characteristic finite element methods are not able to eliminate numerical diffusion entirely.
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  • 28
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 952-952 
    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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  • 29
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 1001-1013 
    ISSN: 0271-2091
    Keywords: Outflow boundary conditions ; Thermal instability ; Richardson extrapolation ; 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 transient two-dimensional Navier-Stokes and energy equations have been solved numerically for flow in a horizontal channel heated from below in the Boussinesq limit. For the set of dimensionless parameters chosen, the flow consists of periodic transverse travelling waves resulting from a convective instability. The solution is proposed as a benchmark for the application of outflow boundary conditions (OBC) in time-dependent flows with strong buoyancy effects. Richardson extrapolation in both time and space is used in obtaining the solution. Field plots and profiles of velocity, temperature, vorticity and streamfunction at selected axial positions and times are also presented from the finest grid and smallest time step calculation. The calculations have been made on an extended domain so that the effects of OBC used in the present study would be negligible in the test region.
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    International Journal for Numerical Methods in Fluids 11 (1990), S. 1075-1095 
    ISSN: 0271-2091
    Keywords: Inexact Newton methods ; Global convergence ; Finite elements ; Full potential equation ; Damping strategies ; 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 computational fluid dynamics, non-linear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these non-linear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modelled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.
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  • 31
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 197-198 
    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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  • 32
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 383-400 
    ISSN: 0271-2091
    Keywords: Circular cylinder ; Impulsively started flow ; Decelerating flow ; Finite difference solution ; Vortex shedding ; Drag and lift coefficients ; 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 study of the unsteady two-dimensional flow past a circular cylinder has been conducted using vorticity and streamfunction as the dependent variables. The two cases considered were impulsively started and decelerated flows. The impulsively started problem was considered to validate the method and has yielded results which agree quite closely with existing results from both calculations and experiments. The decelerated flow analysis produced results which can be explained in terms of induced velocity effects from existing wake vortices for both suddenly stopped and uniformly decelerated flows.
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  • 33
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 491-506 
    ISSN: 0271-2091
    Keywords: Higher-order ; Finite differences ; Navier-Stokes ; 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 discretization scheme is presented which, unlike the standard higher-order finite difference and spline methods, does not give rise to unphysical solution modes and boundary conditions. Practical application of this scheme is achieved via the DCMG algorithm recently developed by the same author, which turns out to be able to find a converged solution of the ψ-ζ Navier-Stokes equations in about the same time for highorder as for low-order discretization schemes. Examples are presented for the driven cavity problem to explore the accuracy of the new method. Finally, a local analysis is performed of the corner singularities which exist in driven cavity flow, and their effect on the overall accuracy of the solutions obtained by polynomial interpolation methods is investigated.
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  • 34
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 577-584 
    ISSN: 0271-2091
    Keywords: Cascade ; Cavitating 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 purpose of this research is to consider the flow through a cascade of bluff bodies, behind which there exist cavities, by using the free streamline theory. When the wake extends to infinity, both the free surface and the velocity on the free surface are unknown and the cavitation number cannot be specified arbitrarily. Given the geometry of the cascade, a numerical method is described in which we obtain the shape of the free surface and the cavitation number. We obtain the relationship between the contraction coefficient, cavitation number and drag coefficient.
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  • 35
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 625-636 
    ISSN: 0271-2091
    Keywords: Single-stage compressor ; Moving grid finite volume method ; Stator-rotor potential interaction ; Inviscid wake-rotor interaction ; 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 generalized finite volume method that can solve the Euler equations for the stator and rotor parts of stage flow in similar formulations is presented. The method consists of a new moving grid finite volume formulation applied to the rotor region and the existing fixed grid finite volume method used in the stator region, with the data transfer made by an interpolation procedure at the sliding surface in between. The accuracy of the method has been demonstrated on a simple cascade flow before the time-dependent compressor stage flow is fully investigated. The transonic stator-rotor flow interaction is elucidated within the inviscid and rotational flow limit.
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  • 36
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 705-708 
    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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  • 37
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 683-704 
    ISSN: 0271-2091
    Keywords: Finite element ; Three-dimensional flows ; Parallelization ; Internal subsonic flows ; Conjugate gradient ; ILU preconditioning ; Uzawa algorithm ; Semi-implicit scheme ; Combustion engine ; Moving 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: In this paper a finite element method is presented to predict internal subsonic flows. Using a low-Mach-number approximation, the pressure is decomposed into a mean thermodynamic contribution and a dynamic fluctuation to deal with the complex role of the pressure in internal aerodynamics. A semi-implicit time integration and a finite element method with a moving mesh are described to take into account complex geometries and moving boundaries. An Uzawa algorithm accelerated by a preconditioned residual method is introduced to solve the coupled non-symmetric linear system for the velocity components and the pressure. An efficient conjugate gradient method combined with an incomplete LU preconditioning is used to solve the non-symmetric linear systems arising from the discretization. The implementation of the numerical scheme on parallel supercomputers is also discussed. Efficient algorithms for the finite element assembly phase and for the solution of linear systems are described which take advantage of the parallel architecture of the new generation of supercomputers. With this technique a global speed-up of 10 is achieved on a supercomputer with eight processors. To illustrate the capabilities of the numerical method, 2D and 3D simulations of flows in the combustion chamber of a reciprocating engine and around the combustor dome of a gas turbine engine are presented.
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  • 38
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 765-783 
    ISSN: 0271-2091
    Keywords: Radiation boundary conditions ; Open boundary conditions ; Wave equation ; 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: On the basis of the dispersion relation of the generalized linear wave equation we derive a radiation boundary condition (RBC) that explicitly incorporates the physical parameters of the governing equation into the form of the boundary condition. Using finite element techniques we investigate the properties of the generalized RBC by examining forced and unforced solutions to the telegraph and Klein-Gordon equations in one dimension. The results show that within the limits of the physical parameters of the problem the generalized RBC is an improvement over the Sommerfeld RBC when the governing equation contains additional terms that influence the propagation. These gains are achieved without introducing any computational overhead. A two-dimensional example suggests that the 1D findings can generalize to higher dimensions.
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  • 39
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    International Journal for Numerical Methods in Fluids 12 (1991), S. 809-823 
    ISSN: 0271-2091
    Keywords: Axisymmetric flow ; Sphere Vortices ; Discrete vortices ; Cloud in 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: A procedure for the calculation of the starting flow around a sphere in a uniform stream is presented. The flow field is simulated by a flow of ideal fluid with embedded vorticity. With the assumption that the flow remains symmetric, the vorticity field is approximated by a number of discrete circular line vortices. The image vortices to satisfy the boundary condition for the normal component of velocity on the surface of the sphere are determined by Butler's sphere theorem. The Stokes streamfunction is used for the field description. The motion of vortices is tracked by the vortex-in-cell method, the cells being formed by square grids.
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  • 40
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 217-233 
    ISSN: 0271-2091
    Keywords: Spectral methods ; Journal bearing problem ; Stokes 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 three-dimensional spectral algorithm for the solution of Stokes flow between eccentrically rotating cylinders is described. Included in the model are pressure boundary conditions at the two ends of the finite length cylinders and the effect of a fluid line source on the inner cylinder. A comparison of results for the load and couple on the inner cylinder is made with those available from lubrication theory in the absence of a line source. Good agreement is shown for long, short and finite journal bearings when the various geometrical assumptions inherent in the lubrication analysis are satisfied.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 269-286 
    ISSN: 0271-2091
    Keywords: Unsteady ; Navier-Stokes ; Domain decomposition ; Schwarz ; QUICK ; Multigrid ; 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 describes a domain decomposition numerical procedure for solving the Navier-Stokes equations in regions with complex geometries. The numerical method includes a modified version of QUICK (quadratic upstream interpolation convective kinematics) for the formulation of convective terms and a central difference scheme for the diffusion terms. A second-order-accurate predictor-corrector scheme is employed for the explicit time stepping. Although the momentum equations are solved independently on each subdomain, the pressure field is computed simultaneously on the entire flow field. A multigrid technique coupled with a Schwarz-like iteration method is devised to solve the pressure equation over the composite domains. The success of this strategy depends crucially on appropriate methods for specifying intergrid pressure boundary conditions on subdomains. A proper method for exchanging information among subdomains during the Schwarz sweep is equally important to the success of the multigrid solution for the overall pressure field. These methods are described and subsequently applied to two forced convection flow problems involving complex geometries to demonstrate the power and versatility of the technique. The resulting pressure and velocity fields exhibit excellent global consistency. The ability to simulate complex flow fields with this method provides a powerful tool for analysis and prediction of mixing and transport phenomenon.
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  • 42
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 599-624 
    ISSN: 0271-2091
    Keywords: Radial turbomachinery ; Inverse design ; Potential 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 fully three-dimensional compressible inverse design method for the design of radial and mixed flow turbomachines is described. In this method the distribution of the circumferentially averaged swirl velocity rVθ on the meridional geometry of the impeller is prescribed and the corresponding blade shape is computed iteratively. Two approaches are presented for solving the compressible flow problem. In the approximate approach the pitchwise variation in density is neglected and as a result the algorithm is simple and efficient. In the exact approach the velocities and density are computed throughout the three-dimensional flow field by employing a fast fourier transform in the tangential direction. The results of the approximate and exact approach are compared for the case of a high-speed (subsonic) radial-inflow turbine and it is shown that the difference between the blade shapes computed by the two methods is well within the manufacturing tolerances. The method was validated by calculating the flow through a designed high-speed radial-inflow turbine by using a three-dimensional inviscid Euler solver. Very good correlation was obtained between the specified and computed rVθ-distributions.
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  • 43
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 775-796 
    ISSN: 0271-2091
    Keywords: Compressible viscous flows ; Implicit methods ; Upwind scheme ; 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: An upwind MUSCL-type implicit scheme for the three-dimensional Navier-Stokes equations is presented and details on the implementation for three-dimensional flows of a ‘diagonal’ upwind implicit operator are developed. Turbulence models for separated flows are also described with an emphasis on the numerical specificities of the Johnson-King non-equilibrium model. Good predictions of separated two- and three-dimensional flows are demonstrated.
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  • 44
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 507-518 
    ISSN: 0271-2091
    Keywords: Multigrid ; Body-fitted co-ordinates ; 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 solution algorithm is described for use on two-dimensional curvilinear meshes generated by the solution of the transformed Laplace equation. The efficiency of the algorithm is improved through the use of a full approximation scheme (FAS) multigrid algorithm using an extended pressure correction scheme as smoother. The multigrid algorithm is implemented as a fixed V-cycle through the grid levels with a constant number of sweeps being performed at each grid level.The accuracy and efficiency of the numerical code are validated using comparisons of the flow over two backward step configurations. Results show close agreement with previous numerical predictions and experimental data. Using a standard Cartesian co-ordinate flow solver, the multigrid efficiency obtainable in a rectangular system is shown to be reproducible in two-dimensional body-fitted curvilinear co-ordinates. Comparisons with a standard one-grid method show the multigrid method, on curvilinear meshes, to give reductions in CPU time of up to 93%.
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  • 45
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 759-773 
    ISSN: 0271-2091
    Keywords: Advection ; Diffusion ; Finite element ; Taylor-least squares ; 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 Taylor-least squares (TLS) scheme, developed to solve the unsteady advection-diffusion equation for advection-dominated cases in one and two dimensions, is extended to three dimensions and applied to some 3D examples to demonstrate its accuracy. The serendipity Hermite element is selected as an interpolation function on a linear hexagonal element. As a validation of the code and as a simple sensitivity analysis of the scheme on the different types of shape functions, the 2D example problem of the previous study is solved again. Four 3D problems, two with advection and two with advection-diffusion, are also solved. The first two examples are advection of a steep 3D Gaussian hill in rotational flow fields. For the advection-diffusion problems with fairly general flow fields and diffusion tensors, analytical solutions are obtained using the ray method. Despite the steepness of the initial conditions, very good agreement is observed between the analytical and TLS solutions.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 797-804 
    ISSN: 0271-2091
    Keywords: Unsteady laminar compressible boundary layer ; Non-iterative finite difference method ; Semisimilarity transformation ; 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 analysis is presented for the unsteady compressible laminar boundary layer driven by a compression or expansion wave. Approximate or series expansion methods have been used for the problems because of the characteristics of the governing equations, such as non-linearity, coupling with the thermal boundary layer equation and initial conditions. Here a transformation of the governing equations and the numerical linearization technique are introduced to deal with the difficulties. First, the governing equations are transformed for the initial conditions by Howarth and semisimilarity variables. These transformations reduce the number of independent variables from three to two and the governing equations from partial to ordinary differential equations at the initial point. Next, the numerical linearization technique is introduced for the non-linearity and the coupling with the thermal boundary layer equation. Because the non-linear terms are linearized without sacrifice of numerical accuracy, the solutions can be obtained without numerical iterations. Therefore the exact numerical solution, not approximate or series expansion, can be obtained. Compared with the approximate or series expansion method, this method is much improved. Results are compared with the series expansion solutions.
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  • 47
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 579-597 
    ISSN: 0271-2091
    Keywords: Diffusion-convection ; Fourier analysis ; Stability ; Artificial viscosity ; 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 stability analysis of second-order, two- and three-time-level difference schemes for the 2D linear diffusion-convection model problem. The corresponding 1D schemes have been extensively analysed in two previous papers by the same author. Most of these 2D schemes obviously generalize 1D schemes, i.e. their stencil only uses the nearest points and defines ‘product difference schemes’; however, the stability results are not always the exact generalization of the 1D stability properties. Moreover, the 1D nonviscous MFTCS scheme may only be generalized if one uses a nine-point scheme. Numerical experiments for different values of the cell Reynolds number allow a comparison to be made between the theoretical and numerical stability limits.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 655-666 
    ISSN: 0271-2091
    Keywords: Two-phase jet ; Gas-liquid spray ; Liquid film ; 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 mathematical hydrodynamic model of a thin liquid film flowing radially on a flat horizontal surface has been elaborated. The model consisted of continuity and momentum equations which were resolved by means of the integral method. In fact, several versions of the model were examined; they differed mainly in film velocity distribution. The predictions of the different versions were then compared with liquid film thicknesses obtained from experimental investigation. The best version was applied in further calculations.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 869-882 
    ISSN: 0271-2091
    Keywords: Flame propagation ; Moving grid method ; Combustion ; Method of lines ; Differential algebraic system ; 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 applications of a moving grid method to the combined problem of ignition and premixed flame propagation in a closed vessel. This method belongs to the general class of adaptive grid techniques for the numerical integration of evolutionary partial differential equations and is based on the method of lines with variable node position. In the present case the motion of the grid and the solution of the partial differential equations are strongly coupled by an implicit formulation. The problem is reduced to an initial value problem for a stiff differential-algebraic system. The continuously moving grid is determined by the equidistribution of a positive function which depends on the solution of the partial differential equations. A differential-algebraic system solver is used for the time integration of the initial value problem. The numerical results of the test problems demonstrate the computational efficiency and the capability of the method to resolve the main features of the solution.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 971-997 
    ISSN: 0271-2091
    Keywords: Unsteady Navier-Stokes ; Composite multigrid method ; Fractional step method ; Staggered grid ; 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 composite multigrid method and its application to a geometrically complex flow. The treatment of the interior boundary conditions within a composite multigrid strategy is described in detail for a 1D model equation. For the Navier-Stokes equations a staggered grid technique is adopted for spatial discretization and a fractional step method is used for the time advance. Lid-driven cavity flows are used to demonstrate the effectiveness of the method.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 1029-1053 
    ISSN: 0271-2091
    Keywords: Grey-body radiation ; Finite element method ; Incompressible fluid flow ; Macrosurfaces ; 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 numerical technique for the simulation of the effects of grey-diffuse surface radiation on the temperature field of fluid flows using FIDAP, a general purpose incompressible, viscous fluid code. The radiating surface relationships assume a non-participating medium, constant surface temperature and heat fluxes at the discretized elemental level.The technique involves the decoupling of energy and radiation exchange equations. A concept of macrosurfaces, each containing a number of radiating boundary surfaces, is introduced. These boundary macroelements then carry the information from the radiating boundary into the fluid regime. A number of simulations illustrating the algorithm are presented.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 1073-1083 
    ISSN: 0271-2091
    Keywords: Crouzeix-Raviart ; Analytical integration ; Brezzi-Babuška condition ; Navier-Stokes ; Finite element 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 methodology for the decomposition of the Crouzeix-Raviart finite element into six linear subelements is described. The resulting element is shown to satisfy the Brezzi-Babuška compatibility condition. The error bounds are also established. A comparison in accuracy between this and the standard Crouzeix-Raviart element is presented for driven cavity flows. Other results include the execution time for the DCR element and the Crouzeix-Raviart element along with both analytical and numerical integration. It is shown that the decomposed element results in shorter execution times with only marginal changes in accuracy.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 805-840 
    ISSN: 0271-2091
    Keywords: Finite element method ; Lagrangian description ; Fractional step method ; Navier-Stokes equation ; Linear interpolation ; 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: This paper presents a finite element analysis based on the Lagrangian description for unsteady incompressible viscous fluid flow with a free surface. The behaviour of the fluid is expressed by the unsteady Navier-Stokes equation. For numerical integration in time the fractional step method is used. This method is useful because one can use the same linear interpolation functions for both velocity and pressure. In this paper, four variations of the fractional step method are presented and the numerical results are compared. To confirm the effectiveness of these methods, solitary wave propagation is analysed.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 883-894 
    ISSN: 0271-2091
    Keywords: Shock capturing ; Steady ; Supersonic ; Isentropic ; 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 scheme is presented for the solution of the two-dimensional equations of steady, supersonic, isentropic flow. The scheme incorporates numerical characteristic decomposition, is shock-capturing by design and incorporates space marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 937-938 
    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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    International Journal for Numerical Methods in Fluids 13 (1991), S. 917-936 
    ISSN: 0271-2091
    Keywords: Magnetohydrodynamics ; CFD ; Thermal buoyancy ; Iterative algorithms ; Explicit algorithms ; 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 complete three-dimensional mathematical model has been developed governing the steady, laminar flow of an incompressible fluid subjected to a magnetic field and including internal heating due to the Joule effect, heat transfer due to conduction, and thermally induced buoyancy forces. The thermally induced buoyancy was accounted for via the Boussinesq approximation. The entire system of eight partial differential equations was solved by integrating intermittently a system of five fluid flow equations and a system of three magnetic field equations and transferring the information through source-like terms. An explicit Runge-Kutta time-stepping algorithm and a finite difference scheme with artificial compressibility were used in the general non-orthogonal curvilinear boundary-conforming co-ordinate system. Comparison of computational results and known analytical solutions in two and three dimensions demonstrates high accuracy and smooth monotone convergence of the iterative algorithm. Results of test cases with thermally induced buoyancy demonstrate the stabilizing effect of the magnetic field on the recirculating flows.
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  • 57
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 999-1028 
    ISSN: 0271-2091
    Keywords: Turbulence ; Channel ; Heat transfer ; Spectral ; Numerical ; 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: Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here.Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.
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  • 58
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    International Journal for Numerical Methods in Fluids 13 (1991) 
    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 13 (1991), S. 1267-1287 
    ISSN: 0271-2091
    Keywords: Micropolar fluid ; Finite element formulation ; Laminar flow ; Constricted tube ; 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 element formulation for the steady laminar flow of an incompressible fluid with microstructure has been developed. The particular fluids considered are commonly known as micropolar fluids, in which case suspended particulate microstructures are modelled by an ‘extended’ continuum formulation. The particle microspin is a new kinematic variable which is independent of the classical vorticity vector and thereby allows relative rotation between particles and the surrounding fluid. This formulation also gives rise to couple stresses in addition to classical force or traction stresses. The finite element formulation utilizes a variational approach and imposes conservation of mass through a penalty function. A general boundary condition for microspin has been incorporated whereby microspin at a solid boundary is constrained to be proportional to the fluid vorticity. The proportionality constant in this case can vary from zero to unity. Sample solutions are presented for fully developed flow through a straight tube and compared with an analytical solution. Results are also generated for flow through a constricted tube and compared with a Newtonian fluid solution.
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  • 60
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    International Journal for Numerical Methods in Fluids 13 (1991), S. 1311-1328 
    ISSN: 0271-2091
    Keywords: Incompressible Navier-Stokes ; Time-dependent ; Moving co-ordinate systems ; Finite volume ; Fractional step ; 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-accurate solution method for the incompressible Navier-Stokes equations in generalized moving coordinates is presented. A finite volume discretization method that satisfies the geometric conservation laws for time-varying computational cells is used. The discrete equations are solved by a fractional step solution procedure. The solution is second-order-accurate in space and first-order-accurate in time. The pressure and the volume fluxes are chosen as the unknowns to facilitate the formulation of a consistent Poisson equation and thus to obtain a robust Poisson solver with favourable convergence properties. The method is validated by comparing the solutions with other numerical and experimental results. Good agreement is obtained in all cases.
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  • 61
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 13-24 
    ISSN: 0271-2091
    Keywords: Streamlined finite elements ; Extrusion ; Free surface flows ; Die design ; Three-dimensional flows ; Three-dimensional 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: A method to determine three-dimensional die shapes from extrudate swell and vice versa is presented using a three-dimensional Galerkin finite element method based on a streamlined formulation with the fluid velocities and pressures represented by triquadratic and trilinear basis functions respectively. The three-dimensional streamlined method, an extension of the two-dimensional formulation, uses successive streamsurfaces to form a boundary-conforming co-ordinate system. This produces a fixd, computational domain leaving the spatial location of the elements as unknowns to be determined with the standard primary variables (u, v, w, p). The extrudate produced by a die of a given shape is considered for moderate Reynolds numbers. Finally, the method is extended to address the problem of die design, where a die profile is sought to produce a target extrudate shape.
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  • 62
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 127-146 
    ISSN: 0271-2091
    Keywords: Numerical simulation ; Slug flow ; Turbulence ; Dissipation ; Open 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: Steps towards the numerical simulation of the flow behind the slug front in horizontal slug flow performed with a streamfunction-vorticity representation of the mean flow and an energy dissipation model for the turbulence are discussed. The flow field consists of two vortices, one saddle point and four stagnation regions. Attention is focused on the following boundary conditions: moving wall jet, moving wall, free jet velocity discontinuity and vertical liquid-gas open surface. A dissipation flux boundary condition is suggested to simulate the interaction of the turbulent eddies with the open surface. A method to assess the necessity to use a transport model equation for the dissipation rather than a geometric specification of a length is suggested. Three different ways to characterize the mixing zone length are proposed.
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  • 63
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 175-187 
    ISSN: 0271-2091
    Keywords: Parallel computing ; Transputer ; CFD ; Fire 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: This paper describes the implementation of a fire field model in the parallel computing environment offered by multiple transputers. The fire model is built into the general purpose SIMPLE-based CFD code HARWELL-FLOW3D. The technique of domain decomposition has been applied tb convert the conventional serial version of FLOW3D into a code capable of efficiently utilizing an arbitrary number of transputers. Fire simulations consisting of up to 24 000 computational cells are performed on parallel systems with up to 15-processors. The run time for this simulation has been reduced from over 4 days on a single processor to just over 8 h on the 15-processor system. An interactive graphics system has also been developed which runs in parallel with the main computations.
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  • 64
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 217-239 
    ISSN: 0271-2091
    Keywords: Swirling flow ; Swirling angle ; Combustion flow ; κ-∊ model ; Algebraic ; Reynolds stress ; 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: Hot flow of a sudden-expansion dump combustor with swirling is analysed by employing an infinite chemical reaction rate. Turbulence properties are closed using one type of algebraic Reynolds stress model and two types of κ-∊ model. One of the κ-∊ models includes a swirling effect modification to the ε-equation. Computations have been performed by the SIMPLE-C algorithm with a power-law scheme. The calculated results of the momentum fields and turbulence quantities for swirling flow are compared with the available experimental data. It is shown that the standard κ-∊ model gives poor prediction of the mean velocity, particularly the tangential velocity. For the hot flow analysis of a sudden-expansion dump combustor with swirling flow it is suggested that it is necessary to use the modified κ-∊ model or algebraic Reynolds stress model.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 267-288 
    ISSN: 0271-2091
    Keywords: Compressible flow ; Hypersonic ; Perfect gas ; Time-dependent ; Convection 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 simple convection algorithm for simulation of time-dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well-known perfect gas flows.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 299-325 
    ISSN: 0271-2091
    Keywords: Compressible gas bearing ; Choked flow ; Finite element 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 theoretical analysis is presented to solve numerically the steady state Navier-Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non-choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.
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  • 67
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 361-374 
    ISSN: 0271-2091
    Keywords: Rapidly varied flow ; Open channel ; Numerical 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: A new method combining the Preissmann four-point scheme and the Holly-Preissmann reach-back scheme is introduced to solve the rapidly varied flow problem in an open channel. The Preissmann four-point scheme is well known for the computation of one-dimensional unsteady flow. The Holly-Preissmann reach-back scheme integrates the Holly-Preissmann two-point scheme with the concept of reach-back characteristics, which allows the characteristics to project several time steps beyond the current time level. A spontaneous surge formation case is used to demonstrate and evaluate the applicability of the new method. It has been found that the results from this method are quite compatible with those of Preissmann four-point scheme. In addition, with the appropriate choice of the number of reach-back time steps, this new method can always avoid the numerical oscillation which usually exists when one uses the Preissmann four-point scheme for the condition of Courant number not close to unity.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 443-457 
    ISSN: 0271-2091
    Keywords: Turbulent oscillating flows ; Finite element method ; The method of averaging ; 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 time-dependent turbulent Navier-Stokes equations are solved numerically by a finite element method with an algebraic eddy viscosity model (Baldwin-Lomax formulation) for oscillating turbulent channel flows. The method of averaging is used to analyse the resulting periodic motion of the fluid. Numerical results are obtained for various Strouhal numbers and relative amplitudes. A comparison is made between the numerical and published experimental results. It appears that for low relative amplitudes in a certain range of frequencies the agreement is satisfactory.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 503-504 
    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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  • 70
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 557-585 
    ISSN: 0271-2091
    Keywords: Multivariant finite element ; Incompressible flow ; Pressure modes ; Shape functions ; 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: Within multivariant elements, which have restricted degrees of freedom at some nodes, different velocity components have different variations. Shape functions for the multivariant elements Q1+ Po and R2+ Po are developed. With such shape functions the value of a velocity component within a multivariant element is shown to depend upon all the independent components of velocity at the nodes of the element.The use of the Q1 P0 element to simulate flows with discontinuous boundary conditions generated disturbance throughout the flow domain, giving erroneous pressure and velocity distributions. The Q1+ Po element restricted the disturbance due to such discontinuities to a small region near the singular points, whereas the P2+ Po element completely eliminated the fluctuations. Flows with discontinuous boundary conditions were simulated with reasonable accuracy by partially relaxing the no-slip condition on the Q1 Po elements near the singular points.
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    International Journal for Numerical Methods in Fluids 14 (1992) 
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    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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    International Journal for Numerical Methods in Fluids 14 (1992), S. 423-441 
    ISSN: 0271-2091
    Keywords: Finite volume method ; Non-orthogonal co-ordinates ; Turbulent recircalating 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 general numerical method for the solution of the complete Reynolds-averaged Navier-Stokes equations for 2D or 3D flows is described. The method uses non-orthogonal co-ordinates, Cartesian velocity components and a pressure-velocity-coupling algorithm adequate for non-staggered grid systems. The capability of the method and the overall performance of the κ-∊ eddy viscosity model are demonstrated by calculations of 2D and 3D flow over a hill. Solution error estimations based on fine grids, e.g. 320 × 192 control volumes, together with comparisons with standard turbulence model modifications, low-Reynoldsnumber or streamline curvature effects, have allowed the investigation of model drawbacks in predicting turbulent flows over surface-mounted hills.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 477-493 
    ISSN: 0271-2091
    Keywords: Bed friction ; Hydrodynamics ; Shallow sea ; Galerkin ; 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 mathematical formulation of a three-dimensional shallow sea model using a modal expansion in the veitical is briefly described.The importance of the time discretization of the vertical diffusion term and bottom friction term is discussed in some detail. Both stability theory and numerical calculations show the importance of time centring or evaluating the modal form of the viscosity term at the higher time step in order to develop a numerically efficient algorithm. Similar analysis and calculations show that in shallow water it is essential to time centre or evaluate bottom friction at the higher time step. In the case of linear bottom friction it is shown that this condition can be readily accomplished. However, using a quadratic friction formulation (a more physically realistic form), this cannot be readily achieved. A new algorithm is presented whereby a stable solution can be obtained even in shallow water using quadratic bottom friction.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1005-1007 
    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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    International Journal for Numerical Methods in Fluids 14 (1992), S. 981-1003 
    ISSN: 0271-2091
    Keywords: Co-ordinate mapping ; Finite element method ; Free-boundary ; 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: A new boundary-conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational fomulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 609-625 
    ISSN: 0271-2091
    Keywords: 3D extrusion ; Moving boundaries ; Kinematic condition ; Remeshing ; Finite elements ; Free surfaces ; 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 numerical technique for solving three-dimensional free surface problems in extrusion applications. The method is fully implicit in the sense that a Newton-Raphson scheme is applied on all variables, and geometrically general. In particular, the die section shape may be complex and contains multiple corners: very few restrictions apply on the mesh generation because the method does not require the nodes to be located on straight lines (spines). A clear distinction is introduced between the directions associated with the kinematic condition and the remeshing rules. As a difference with respect to earlier publications, these concepts are handled separately. Only Stokes problems are solved in this paper and we have not introduced surface tension. Therefore corners in the die section propagate discontinuities in the extrudate shape, an a method for relocating corners without losing the quadratic convergence of the scheme is presented. Data structures used for the implementation are briefly discussed.We present results on the extrusion of various profiles, including a rectangular die (a benchmark problem) and various complex sections containing multiple corners.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1009-1018 
    ISSN: 0271-2091
    Keywords: Mathematical modeling ; Shock capturing ; Upwind schemes ; Flux difference splitting ; Open channel 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 upwind finite difference scheme based on flux difference splitting is presented for the solution of the equations governing unsteady open channel hydraulics. An approximate Jacobian needed for splitting the flux differences is defined that satisfies the conditions required to construct a first-order upwind conservative discretization of the equations. Added limited second-order corrections make the resulting scheme robust and accurate for the computation of all regimes of open channel flow. Some numerical results and comparisons with other classical schemes under exacting conditions are presented.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1063-1086 
    ISSN: 0271-2091
    Keywords: Boundary element method ; Local mesh refinement ; Convergence ; Small interparticle gap ; Adaptive subdomain integration ; Superparametric ; 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 boundary element technique was developed to simulate the 3D hydrodynamic interactions between multiple particles of arbitrary shape. This paper reports the results of an extensive validation procedure aimed at demonstrating the convergence characteristics of the technique, especially in cases where the particles are in close proximity. The quadratic elements are superior to the lower-order elements in terms of accuracy, computer storage and CPU time required, thus resulting in a significant improvement in the overall computational efficiency. Superparametric discretization improves the accuracy over isoparametric discretization but lowers the convergence rate of the method. When the interparticle gap becomes very small (less than 1% of the particle radius), the numerical solution diverges owing to inaccurate determination of the element contributions in the gap region. An adaptive subdomain integration scheme was developed that dramatically improved the integration accuracy and provided convergent solutions for problems of very small gaps down to 0-01% of the particle diameter.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1111-1130 
    ISSN: 0271-2091
    Keywords: Non-linear waves ; Diffraction ; Wave forces ; Circular cylinder ; Grid generation ; Numerical 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: The interaction of two-dimensional water waves with a fixed submerged cylinder is studied using a finite difference scheme with boundary-fitted co-ordinates. A mixed Eulerian-Lagrangian (MEL) formulation is used to satisfy the fully non-linear free surface conditions. The diffraction of small-amplitude water waves by a cylinder is examined for various wavelengths and amplitudes of the incident wave. Fourier analyses of the incident and diffracted waves are performed to determine their spectra. An example of a large-amplitude wave breaking over a cylinder is also studied. The non-linear numerical solutions are compared with those of experiments and linear theory where appropriate.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1151-1171 
    ISSN: 0271-2091
    Keywords: Shock tubes ; Boundary layers ; Roe's scheme ; Navier-Stokes ; 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 scheme is used to investigate boundary layer effects in a shock tube. The method consists of a mixture of Roe's approximate Riemann solver and central differences for the convective fluxes and central differences for the viscous fluxes and is implicit in one space dimension. Comparisons are made with experimental data and with solutions obtained via boundary layer equations. Examination of the calculated flow field explains the observed behaviour and highlights the approximate nature of boundary layer solutions.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1135-1149 
    ISSN: 0271-2091
    Keywords: Free surface flow ; Non-linear effects ; Free surface boundary layer ; BEM ; 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 non-linear free surface potential flow past a 2D non-lifting body is computed. The numerical method is based on the simple layer integral formulation; the non-linear solution is obtained by means of an iterative procedure. Under some hypotheses, viscosity effects at the free surface are considered. All the numerical results obtained have been tested against analytical solutions and experimental results.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 817-841 
    ISSN: 0271-2091
    Keywords: Mixed convection ; Finite elements ; CVD ; Iterative methods ; Preconditioning ; 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 is presented for the finite element solution of three-dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMERS), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centered around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain-renumbering scheme that enhances the overall algorithm performance is proposed on the basis of and analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly f the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three-dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.
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  • 83
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1325-1345 
    ISSN: 0271-2091
    Keywords: κ-∊ ; Wall functions ; Finite element ; 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 extended κ-∊ model (to include low-Reynolds-number regions) employing weighting functions is presented. Wall functions for the near-wall zones are developed giving correct boundary values for the Shear stress and κ-∊. A finite element model using a penalty formulation for incompressible turbulent flow is applied to Solve a flow between two plates. Results with mesh boundaries situated in the near-wall region and a: the wall are compared with measured values.
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  • 84
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 427-451 
    ISSN: 0271-2091
    Keywords: Aerodynamics ; Rotor ; Blade-vortex ; Interactions ; 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 procedure has been developed for the prediction of three-dimensional rotor blade-vortex interactions. The interaction velocity field was obtained through a non-linear superposition of the rotor flow field, computed using the unsteady three-dimensional Euler equations, and the embedded vortex wake flow field, computed using the law of Biot-Savart. In the Euler model, near wake rotational effects were simulated using the surface velocity ‘transpiration’ approach. As a result, a modified surface boundary condition was prescribed and enforced at each time step of the computations to satisfy the tangency boundary condition. For supercritical interactions using an upstream-generated vortex, accuracy of the numerical results were found to rely on the user-specified vortex core radius and vortex strength. For the more general self-generated subcritical interactions, vortex wake trajectories were computed using the lifting-line helicopter/rotor trim code CAMRAD. For these interactions, accuracy of the results were found to rely heavily on the CAMRAD-predicted vortex strength, vortex orientation with respect to the blade, and to a large extent on the user-specified vortex core radius. Results for the one-seventh scale model OLS rotor and for a non-lifting rectangular blade having a NACA0012 section are presented. Comparisons with the experimental windtunnel data are also made.
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  • 85
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 503-524 
    ISSN: 0271-2091
    Keywords: Spin-up ; Viscous flow ; Time-dependent ; Ekman layers ; Finite volume ; Fractional step ; 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 addresses the spin-up from rest of a free-surface fluid confined in a cylindrical container with a semicircular cross-section. The flow in the various stages of the spin-up process has been calculated numerically by using the finite-volume technique on a three-dimensional grid. Local grid refinement was applied in order to capture the effects of the boundary layer at the lateral boundaries and of the Ekman layer at the bottom. The numerical results agree very well with laboratory observations.
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  • 86
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 525-544 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Mixed formulation ; Orthomin ; Bi-CGSTAB ; Jacobi preconditioning ; SSOR ; 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 paper, preconditioning of iterative equation solvers for the Navier-Stokes equations is investigated. The Navier-Stokes equations are solved for the mixed finite element formulation. The linear equation solvers used are the orthomin and the Bi-CGSTAB algorithms. The storage structure of the equation matrix is given special attention in order to avoid swapping and thereby increase the speed of the preconditioner. The preconditioners considered are Jacobian, SSOR and incomplete LU preconditioning of the matrix associated with the velocities. A new incomplete LU preconditioning with fill-in for the pressure matrix at locations in the matrix where the corner nodes are coupled is designed. For all preconditioners, inner iterations are investigated for possible improvement of the preconditioning. Numerical experiments are executed both in two and three dimensions.
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  • 87
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 613-623 
    ISSN: 0271-2091
    Keywords: Large sparse non-symmetric linear system ; Multilevel iteration ; Generalized minimal residual method ; Parallel computing ; Distributed memory ; 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: Linearization of the non-linear systems arising from fully implicit schemes in computational fluid dynamics often result in a large sparse non-symmetric linear system. Practical experience shows that these linear systems are ill-conditioned if a higher than first-order spatial discretization scheme is used. To solve these linear systems, an efficient multilevel iterative method, the α-GMRES method, is proposed which incorporates a diagonal preconditioning with a damping factor α so that a balanced fast convergence of the inner GMRES iteration and the outer damping loop can be achieved. With this simple and efficient preconditioning and damping of the matrix, the resulting method can be effectively parallelized. The parallelization maintains the effectiveness of the original scheme due to the algorithm equivalence of the sequential and the parallel versions.
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  • 88
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 955-957 
    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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  • 89
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 99-124 
    ISSN: 0271-2091
    Keywords: Wing-body junction ; Horseshoe vortex flow ; Numerical solution ; Navier-Stokes equations ; Viscous-inviscid interaction ; 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 computation of the incompressible three-dimensional turbulent viscous flow about an aerofoil/flat plate junction is investigated. An iterative, fully decoupled technique is applied to the Reynolds-averaged Navier-Stokes equations (RANSEs) written in a non-orthogonal curvilinear body-fitted co-ordinate system. The results of the computations are compared with well-documented experiments.
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  • 90
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    International Journal for Numerical Methods in Fluids 15 (1992) 
    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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  • 91
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 925-952 
    ISSN: 0271-2091
    Keywords: CFD ; Potential transonic flow ; Streamwise co-ordinates ; Shock point operator ; 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 approach to calculate transonic flows is developed. A set of full-potential-equivalent equations in the von Mises co-ordinate system is formulated under the irrotationality and isentropic assumptions. The emphasis is placed on supercritical flow, in which the treatment of embedded shock waves is crucial to get convergent solutions. Shock jump conditions are employed and shock point operators (SPOs) are constructed in the body-fitting streamline co-ordinate system. SPOs and a type-dependent difference scheme are applied to solve the ‘main’ equation for the ‘main’ variable, the streamline ordinate y. A number of ‘secondary’ equations are deduced for the corresponding ‘secondary’ variables. An optimal combination for the ‘secondary’ variable, its equation and related difference scheme is selected to be the generalized density R, its linear equation and the Crank-Nicolson scheme. Numerical results show that the present approach gives good agreement with experimental data and other computational work for NACA0012 and biconvex aerofoils in both subcritical and supercritical ranges.
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  • 92
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 975-984 
    ISSN: 0271-2091
    Keywords: Natural convection ; Forced convection ; Porous medium ; Numerical modelling ; CFD package ; 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 PC-based system for modelling of convection in enclosures on the basis of the Navier-Stokes equations is described and a number of test results are given. New examples of mixed convection in a square chamber and thermal convection in ordinary and porous (isotropic and anisotropic) vertical layers are presented which may be of interest in civil and building engineering.
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  • 93
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1333-1355 
    ISSN: 0271-2091
    Keywords: Multigrid ; Domain decomposition ; Flux splitting ; Deferred corrector ; 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 application of grid stretching or grid adaptation is generally required in order to optimize the distribution of nodal points for fluid-dynamic simulation. This is necessitated by the presence of disjoint high gradient zones, that represent boundary or free shear layers, reversed flow or vortical flow regions, triple deck structures, etc. A domain decomposition method can be used in conjunction with an adaptive multigrid algorithm to provide an effective methodology for the development of optimal grids. In the present study, the Navier-Stokes (NS) equations are approximated with a reduced Navier-Stokes (RNS) system, that represents the lowest-order terms in an asymptotic Re expansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and ensures mass conservation in all subdomain grid interfaces, as well as at the outflow boundary. The higher-order (NS) diffusion terms are included through a deferred corrector, in selected subdomains, when necessary. Adaptivity in the direction of refinement is achieved by grid splitting or domain decomposition in each level of the multigrid procedure. Normalized truncation error estimates of key derivatives are used to determine the boundaries of these subdomains. The refinement is optimized in two co-ordinate directions independently. Multidirectional adaptivity eliminates the need for grid stretching so that uniform grids are specified in each subdomain. The overall grid consists of multiple domains with different meshes and is, therefore, heavily graded. Results and computational efficiency are discussed for the laminar flow over a finite length plate and for the laminar internal flow in a backward-facing step channel.
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  • 94
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1383-1406 
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Co-volume method ; Upwind ; Voronoi tessellation ; Networks ; 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 dual variable method for Delaunay triangulations is a network-theoretic method that transforms a set of primitive variable finite difference or finite element equations for incompressible flow into an equivalent system which is one-fifth the size of the original. Additionally, it eliminates the pressures from the system and produces velocities that are exactly discretely divergence-free. In this paper new discretizations of the convection term are presented for Delaunay triangulations, the dual variable method is extended to tessellations that contain obstacles, and an efficient algorithm for the solution of the dual variable system is described.
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  • 95
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1421-1422 
    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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  • 96
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    International Journal for Numerical Methods in Fluids 16 (1993), S. 29-42 
    ISSN: 0271-2091
    Keywords: 3D extrusion ; Moving boundaries ; Die design ; Remeshing ; Finite elements ; Free surfaces ; 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: Let us call a direct extrusion problem (DEP) the problem of finding the shape of the extrudate coming out of a die of prescribed shape. An implicit finite element formulation of the DEP which is geometrically general and for which a Newton-Raphson technique can be implemented has recently been proposed by Legat and Marchal. However, the problem posed to the die designer is frequently the inverse extrusion problem (IEP), i.e. finding the die shape which produces an extrudate of prescribed shape. This paper presents an extension of our original method for solving the IEP which avoids the ‘trial-and-error’ iteration on the die geometry itself.The advantage of the formulation lies in its capability to handle complex geometrics and in its low cost, because the CPU time and memory required to solve the IEP are almost identical to those of the DEP. We present benchmark results for squares and rectangles and new results obtained for geometries involving multiple corners. For an octagonal shape we also consider the case of a power-law fluid.For all results presented in this paper, surface tension has not been included.
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  • 97
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    International Journal for Numerical Methods in Fluids 16 (1993) 
    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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  • 98
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    International Journal for Numerical Methods in Fluids 16 (1993), S. 105-131 
    ISSN: 0271-2091
    Keywords: Tidal-currents ; Stratification ; Galerkin ; Spectral ; Log-layer ; Resolution ; B-spline ; 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 deals with the accurate determination of tidal current profiles in both homogeneous and stratified regions when a no-slip condition is used at the seabed with a flow-dependent eddy viscosity related to the depth-mean current or the bed frictional velocity.Calculations show that it is essential to accurately resolve the high-shear region which occurs at the bed and across the pycnocline/thermocline in the case of stratified flow. A computationally accurate and economic method of resolving these regions is demonstrated using the Galerkin method with a set of basis functions designed to accurately reproduce the high-shear layers which occur in these regions.With a flow-independent eddy viscosity a stability analysis can be readily performed and an unconditionally stable algorithm developed. However, with a flow-dependent viscosity, in particular a viscosity computed from the frictional velocity, a non-linear numerical instability can occur. A method of maintaining numerical stability in this case is also described.The importance of near-bed resolution to the computed value of the frictional velocity is demonstrated and its influence on the total tidal velocity profile is illustrated by a number of idealized calculations using various eddy viscosity formulations.The influence of stratification on the computed tidal profiles is shown in the latter part of the paper.
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  • 99
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    International Journal for Numerical Methods in Fluids 16 (1993) 
    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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  • 100
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    International Journal for Numerical Methods in Fluids 16 (1993), S. 231-237 
    ISSN: 0271-2091
    Keywords: Compressible flows ; Boundary integral equation method ; Fundamental-solution method ; Non-linear potential 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 complete boundary integral formulation for steady compressible inviscid flows governed by non-linear equations is established by using the specific mass flux as a dependent variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain. It is shown that the boundary integral formulation developed in this paper is equivalent of the results of distributions of the fundamental solutions of the Laplacian operator equation with a different order along the boundaries of the domain. Hence, we have succeeded in establishing the fundamental-solution method for compressible inviscid flows governed by non-linear equations.
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