Abstract
Steady Euler- and Navier-Stokes equations are discretized with a vertex-centered finite volume method. For the definition of the convective fluxes, a flux-difference splitting upwind method, based on the polynomial character of the flux-vectors with respect to the primitive variables is used. The diffusive fluxes are defined in the classical central way.
In the first order formulation, flux-difference splitting leads to a discretization of vector-positive type. This allows a solution by classical relaxation methods in multigrid form.
By the use of the flux-difference splitting concept a consistent discrete formulation of boundary conditions, including the treatment of diffusive fluxes, is possible for all types of boundaries: in- and outflow and solid boundaries. A second order formulation is achieved by using a limited flux-difference extrapolation according to the method suggested by Chakravarthy and Osher. The minmod-limiter is used. In second order form, direct relaxation of the discrete equations is not possible anymore due to the loss of positivity. To solve the second order system, defect-correction is used.
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Dick, E. (1991). Multigrid Methods for Steady Euler- and Navier-Stokes Equations Based on Polynomial Flux-Difference Splitting. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5712-3_1
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DOI: https://doi.org/10.1007/978-3-0348-5712-3_1
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