A non-parametrized entropy correction for Roe's approximate Riemann solver
type: Item
instance of: scholarly article
title: A non-parametrized entropy correction for Roe's approximate Riemann solver
zbMATH Open document ID: 0861.65073
author: Francois Dubois
author: Guillaume Mehlman
published in: Numerische Mathematik
publication date: 1997-04-24T00:00:00Z
review text: The approximate Riemann solver of \textit{P. L. Roe} [J. Comput. Phys. 43, 357-372 (1981; Zbl 0474.65066)] is improved. A new nonparameterized approach is proposed which is based on a nonlinear Hermite interpolation of an approximate flux function and the exact resolution of nonconvex scalar Riemann problems. Convergence and consistency with the entropy condition are proved for scalar convex conservation laws with arbitrarily large initial data. For strictly hyperbolic systems of conservation laws consistency of the resulting scheme with the entropy condition is also proved for initial data sufficiently close to a constant. A one-dimensional shock-tube and a two-dimensional supersonic forward facing step are considered as examples.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 932037
zbMATH Keywords: convergence
zbMATH Keywords: Riemann solver
zbMATH Keywords: nonlinear Hermite interpolation
zbMATH Keywords: consistency
zbMATH Keywords: entropy condition
zbMATH Keywords: conservation laws
zbMATH Keywords: hyperbolic systems
reviewed by: Plamen Yalamov
MaRDI profile type: Publication
full work available at URL: s002110050190
OpenAlex ID: W2321308174
DOI: 10.1007/S002110050190
description: scientific article; zbMATH DE number 932037