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  • 1
    Electronic Resource
    Electronic Resource
    An assessment of the finite termination property of the defect correction method (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 199-215 
    Details
    ISSN: 0271-2091
    Keywords: Defect correction ; Conservation laws ; 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 investigates the use of defect correction procedures for the solution of finite volume approximations to systems of conservation laws. Particular emphasis is laid on the order of accuracy obtained after a fixed finite number of iterations. It is shown that a high order of accuracy may be achieved after only one defect correction iteration, involving two inversions of a stable lower-order-accurate operator. However, this result is found to be critically dependent on the consistency of the lower-order operator, a property which does not always hold for conservative finite volume discretizations. Through numerical experiments, the lack of consistency of these schemes is found to inhibit severely the finite termination property of the defect correction process. Results are presented for linear advection, Poisson's equation, and the Euler equations.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650160304
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A vertex-centred finite volume method with shock detection (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 605-625 
    Details
    ISSN: 0271-2091
    Keywords: Vertex-centred ; Finite volume ; Multigrid ; Navier-Stokes ; Shock detection ; Turbulence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper introduces a vertex-centred finite volume method for compressible viscous flow incorporating a new shock detection procedure. The discretization is designed to be robust and accurate on the highly stretched and curved meshes necessary for resolving turbulent boundary layers around the leading edge of an aerofoil. Details of the method are described for two-dimensional problems and the natural extension of three-dimensional multiblock meshes is discussed. The shock detection procedure is used to limit the range of the shock-capturing dissipation specifically to regions containing shocks. For transonic turbulent flow this is shown to improve the boundary layer representation significantly.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180605
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Cell vertex finite volume discretizations in three dimensions (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 505-527 
    Details
    ISSN: 0271-2091
    Keywords: Cell vertex ; Accuracy on parallelepipeds ; Triangulated control volumes ; 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 cell vertex method is generalized to three dimensions. It is proved that there exists a one-parameter family of eight-point three-dimensional methods with second-order truncation error on parallelepipeds. Using different triangulations of control volume faces, various finite volume methods are derived. Some of these are identified as members of the aforementioned one-parameter family and may be regarded as second-order upwind schemes. A Fourier analysis is used to investigate the spectral properties of these discretizations.Numerical experiments illustrate that second-order global accuracy is achieved on parallelepiped grids, as suggested by the theory. Randomly perturbed, stretched, sheared meshes are used to test these methods to destruction. It is found that upwinding improves both the accuracy on distorted meshes and the spectrum of the discretization.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140502
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Implicit time-accurate solutions on unstructured dynamic grids (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 1285-1300 
    Details
    ISSN: 0271-2091
    Keywords: multigrid ; Euler ; unsteady ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper an unstructured multigrid algorithm is used as an iterative solution procedure for the discrete equations arising from an implicit time discretization of the unsteady Euler equations on tetrahedral grids. To calculate unsteady flows due to oscillating boundaries, a novel grid movement algorithm is introduced in which an elliptic equation with a non-linear diffusion coefficient is used to define the displacement of interior grid nodes. This allows large grid displacements to be calculated in a single step. The multigrid technique uses an edge-collapsing algorithm to generate a sequence of grids, and a pseudo-time-stepping smoother. On the coarser grids, no grid motion is used. Instead, surface normals are rotated consistently and transfer/interpolation weights are based on the time-averaged grid co-ordinates. A 2D NACA0012 test case is used to validate the programme. 3D results are presented for the M6 wing and a full aircraft configuration. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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