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Computing Flow on General Two-Dimensional Nonsmooth Staggered Grids (1998)

Wesseling, P. ; Segal, A. ; Kassels, C.G.M. ; [et al.]

Springer

Journal of engineering mathematics 34 (1998), S. 21-44

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ISSN: 1573-2703

Keywords: Navier-Stokes ; finite volume discretization ; staggered grids ; boundary-fitted coordinates.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Technology

Notes: Abstract The classical staggered scheme for the incompressible Navier-Stokes equations is generalized from Cartesian grids to general boundary-fitted structured grids. The resulting discretization is coordinate-invariant. The unknowns are the pressure and the contravariant volume flux components. The grid can be strongly nonuniform and nonorthogonal. The smoothness properties of the coordinate mapping are carefully taken into account. As a result, the accuracy on rough grids is found to be at least as good as for typical finite element and nonstaggered finite volume schemes. Extension to compressible flows results in a scheme with Mach-uniform accuracy and efficiency for Mach numbers ranging from M = 0 to M 〉 1. Accurate discretization of two-equation turbulence models is also possible.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1004341115180

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Invariant discretization of the incompressible Navier-Stokes equations in boundary fitted co-ordinates (1992)

Segal, A. ; Wesseling, P. ; Van Kan, J. ; [et al.]

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 15 (1992), S. 411-426

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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.