Roe solver with entropy corrector for uncertain hyperbolic systems

J. Tryoen, O. Le Maître, M. Ndjinga, A. Ern*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

This paper deals with intrusive Galerkin projection methods with a Roe-type solver for treating 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. We derive some indicators that can be used to decide where a correction is needed, thereby reducing the computational costs considerably. The effectiveness of the proposed corrector is assessed on the Burgers and Euler equations including sonic points.

Original languageEnglish (US)
Pages (from-to)491-506
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume235
Issue number2
DOIs
StatePublished - Nov 15 2010

Keywords

  • Conservation laws
  • Entropy correction
  • Galerkin projection
  • Hyperbolic systems
  • Roe solver
  • Stochastic spectral methods
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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