Developments of entropy-stable residual distribution methods for conservation laws I: scalar problems

Ismail, Farzad and Chizari, Hossain ORCID: https://orcid.org/0000-0002-6630-1880 2017. Developments of entropy-stable residual distribution methods for conservation laws I: scalar problems. Journal of Computational Physics 330 , pp. 1093-1115. 10.1016/j.jcp.2016.10.065

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Abstract

This paper presents preliminary developments of entropy-stable residual distribution methods for scalar problems. Controlling entropy generation is achieved by formulating an entropy conserved signals distribution coupled with an entropy-stable signals distribution. Numerical results of the entropy-stable residual distribution methods are accurate and comparable with the classic residual distribution methods for steady-state problems. High order accurate extensions for the new method on steady-state problems are also demonstrated. Moreover, the new method preserves second order accuracy on unsteady problems using an explicit time integration scheme. The idea of the multi-dimensional entropy-stable residual distribution method is generic enough to be extended to the system of hyperbolic equations, which will be presented in the sequel of this paper.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Publisher:	Elsevier
ISSN:	0021-9991
Date of Acceptance:	29 October 2016
Last Modified:	05 Nov 2022 02:42
URI:	https://orca.cardiff.ac.uk/id/eprint/135207

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