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A Genuinely multidimensional Riemann solver

Remi Abgrall 1
1 SINUS - Numerical Simulation for the Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Many model numerical method for the integration of the equation of compressible flows rely on TVD type schemes with Riemann solvers. These schemes are directly built from the generalisation of 1D numerical schemes for the Euler equations by mean of the finite volume method. Doing this, some propagation directions are privileged, the directions orthogonal to the facets of the control volumes. This may lead to large numerical errors, especially xhen the mesh is distorted. In this report, we compute the exact solution of the Riemann for a linear hyperbolic equation obtained from the Euler equation by linearisation. Then, we show how to apply this result to construct a first order finit volume scheme that is genuinely multidimensional
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https://hal.inria.fr/inria-00074814
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 4:28:43 PM
Last modification on : Saturday, January 27, 2018 - 1:31:33 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:01:56 PM

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  • HAL Id : inria-00074814, version 1

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Remi Abgrall. A Genuinely multidimensional Riemann solver. [Research Report] RR-1859, INRIA. 1993, pp.20. ⟨inria-00074814⟩

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