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

Ismail, Farzad and Chizari, Hossain 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: 19 Oct 2021 01:22
URI: https://orca.cardiff.ac.uk/id/eprint/135207

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