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Three-Dimensional Adaptive Central Schemes on Unstructured Staggered Grids

In: Hyperbolic Problems: Theory, Numerics, Applications

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  • A. Madrane

    (Airbus/Institute for Aerospace-Technology)

Abstract

We present a new formulation of three-dimensional central finite volume methods on unstructured staggered grids for solving systems of hyperbolic equations. Based on the Lax–Friedrichs and Nessyahu–Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve a staggered grids to avoid solving Riemann problems at cell interfaces. The cells are barycentric, while those of the staggered grid are diamond shaped. To reduce artificial viscosity, we start with an adaptively refined primal grid in three-dimensional, where the theoretical a posteriori result of the first-order scheme is used to derive appropriate refinement indicators.We apply those methods and solve Euler equations. Our numerical results are in good agreement with corresponding results appearing in the literature.

Suggested Citation

  • A. Madrane, 2008. "Three-Dimensional Adaptive Central Schemes on Unstructured Staggered Grids," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 703-710, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_71
    DOI: 10.1007/978-3-540-75712-2_71
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