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

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• 作者：Farzad Ismail ; ^{aefarzad@usm.my} ; Hossain Chizari ^{hc12_aer008@student.usm.my hossainchizari@gmail.com}
• 关键词：Entropy conservation ; Entropy-stable ; Residual distribution ; Semi-discrete ; Scalar advection
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：1093-1115
• 全文大小：1052 K
• 卷排序：330

文摘

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.