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On the behavior of upwind schemes in the low Mach number limit. IV : P0 Approximation on triangular and tetrahedral cells

Hervé Guillard 1
1 SMASH - Simulation, modeling and analysis of heterogeneous systems
CRISAM - Inria Sophia Antipolis - Méditerranée , Université de Provence - Aix-Marseille 1
Abstract : Finite Volume upwind schemes for the Euler equations in the low Mach number regime face a problem of lack of convergence toward the solutions of the incompressible system. However, if applied to cell centered triangular grid, this problem disappears and convergence toward the incompressible solution is recovered. We give here a general proof of this fact for arbitrary unstructured meshes. In addition, we also show that this result is equally valid for unstructured three dimensional tetrahedral meshes.
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https://hal.inria.fr/inria-00374925
Contributor : Herve Guillard <>
Submitted on : Friday, April 10, 2009 - 2:47:05 PM
Last modification on : Saturday, January 27, 2018 - 1:31:28 AM
Long-term archiving on: : Thursday, June 10, 2010 - 8:18:19 PM

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Hervé Guillard. On the behavior of upwind schemes in the low Mach number limit. IV : P0 Approximation on triangular and tetrahedral cells. [Research Report] RR-6898, INRIA. 2009, pp.14. ⟨inria-00374925⟩

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