HAL : hal-00444845, version 1

DOI : 10.1016/j.cam.2010.05.043

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Journal of Computational and Applied Mathematics 235, 2 (2010) 491-506

Roe Solver with Entropy Corrector for Uncertain Hyperbolic Systems

Julie Tryoen 1, 2, Olivier Le Maitre 2, Michael Ndjinga 3, Alexandre Ern 1

(15/11/2010)

This paper deals with intrusive Galerkin projection methods with Roe-type solver for uncertain hyperbolic systems using a finite volume discretization in physical space and a piecewise continuous representation at the stochastic level. The aim of this paper is to design a cost-effective adaptation of the deterministic Dubois and Mehlman corrector to avoid entropy-violating shocks in the presence of sonic points. The adaptation relies on an estimate of the eigenvalues and eigenvectors of the Galerkin Jacobian matrix of the deterministic system of the stochastic modes of the solution and on a correspondence between these approximate eigenvalues and eigenvectors for the intermediate states considered at the interface. Some indicators are derived to decide where a correction is needed, thereby reducing considerably the computational costs. The effectiveness of the proposed corrector is assessed on the Burgers and Euler equations including sonic points.

1 :	Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
	Ecole des Ponts ParisTech
2 :	Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI)
	CNRS : UPR3251 – Université Paris VI - Pierre et Marie Curie
3 :	Laboratoire de Génie Logiciel et de Simulation (LGLS)
	CEA : DEN/DM2S/SFME/LGLS

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : Uncertainty Quantification – hyperbolic systems – conservation laws – stochastic spectral methods – Galerkin projection – Roe solver – entropy correction

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Contributeur : Julie Tryoen <>

Soumis le : Jeudi 7 Janvier 2010, 13:58:05

Dernière modification le : Vendredi 4 Novembre 2011, 11:57:26