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  • 1
    Electronic Resource
    Electronic Resource
    Benchmark solutions for the incompressible Navier-Stokes equations in general co-ordinates on staggered grids (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 301-321 
    Details
    ISSN: 0271-2091
    Keywords: Benchmark solution ; Incompressible Navier-Stokes ; Staggered grid ; General co-ordinates ; 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: Benchmark problems are solved with the steady incompressible Navier-Stokes equations discretized with a finite volume method in general curvilinear co-ordinates on a staggered grid. The problems solved are skewed driven cavity problems, recently proposed as non-orthogonal grid benchmark problems. The system of discretized equations is solved efficiently with a non-linear multigrid algorithm, in which a robust line smoother is implemented. Furthermore, another benchmark problem is introduced and solved in which a 90° change in grid line direction occurs.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170404
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Invariant discretization of the incompressible Navier-Stokes equations in boundary fitted co-ordinates (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 411-426 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Incompressible ; Boundary-fitted co-ordinates ; Boundary conditions ; Invariant discretization ; 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 discretization of the incompressible Navier-Stokes equation on boundary-fitted curvilinear grids is considered. The discretization is based on a staggered grid arrangement and the Navier-;Stokes equations in tensor formulation including Christoffel symbols. It is shown that discretization accuracy is much enhanced by choosing the velocity variables in a special way. The time-dependent equations are solved by a pressure-correction method in combination with a GMRES method. Special attention is paid to the discretization of several types of boundary conditions. It is shown that fairly non-smooth grids may be used using our approach.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150404
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    FLUX DIFFERENCE SPLITTING FOR THREE-DIMENSIONAL STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN CURVILINEAR CO-ORDINATES (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 347-366 
    Details
    ISSN: 0271-2091
    Keywords: three-dimensional incompressible Navier-Stokes ; collocated grid ; curvilinear co-ordinates ; flux difference splitting ; defect correction ; 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: A collocated discretization of the 3D steady incompressible Navier-Stokes equations based on a flux-difference-splitting formulation is presented. The discretization employs primitive variables of Cartesian velocity components and pressure. The splitting used here is a polynomial splitting introduced by Dick and Linden of Roe type. Second-order accuracy is obtained with the defect correction approach in which the state vector is inter-polated with van Leer's κ-scheme. The underlying solution technique to solve the discretized equations is a parallel multiblock multigrid method. Several 2D and 3D test problems such as driven cavity and channel flows are solved.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    Steady incompressible flow around objects in general coordinates with a multigrid solution method (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 10 (1994), S. 295-308 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Steady incompressible flow around objects in general coordinates is investigated. First, an overview of the popular approaches to discretize incompressible flow problems in general coordinates is given. It has been chosen to solve the equations on a staggered grid with contravariant flux unknowns and pressure as primitive variables. A solution method multigrid is used, with a line smoother able to deal with stretched cells. For flow problems around objects solved with a single block discretization periodic boundary, conditions are prescribed and adaptations for the discretization and the multigrid method are given. Steady flow around a circular cylinder and around an ellipse are presented. © 1994 John Wiley & Sons, Inc.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690100304
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    Paper (German National Licenses)
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