高阶保号熵稳定格式

Abstract

Abstract:

Ensuring the sign preserving on entropy variable after the high-order reconstruction is fundamental in constructing the high-order entropy stable schemes. In this paper, we construct the 3rd order compact CWENO-type entropy stable schemes (Fjordholm's the 3rd order entropy conservative schemes with sign preserving compact CWENO reconstruction for the entropy variable) and prove the sign preserving on entropy variable with the 3rd order compact CWENO reconstruction. Numerical results show that the schemes can achieve third-order accuracy, and have high resolution, robustness and non-oscillation.

Key words: Sign preserving, Compact CWENO reconstruction, Entropy stable schemes

CLC Number:

O354

Supei Zheng,Xia Xu,Jianhu Feng,Dou Jia. High Order Sign Preserving Entropy Stable Schemes[J].Acta mathematica scientia,Series A, 2021, 41(5): 1296-1310.

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References 23

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N	L¹ error	Rate	L^∞ error	Rate
40	0.001979313043305		3.629516311932702e-04
80	2.726027476503843e-04	2.86	7.092855086397350e-05	2.36
160	3.522356279884232e-05	2.95	9.975669895746602e-06	2.83
320	4.405706993699641e-06	3.00	1.260137438287312e-06	2.99
640	5.373835462491922e-07	3.01	1.576597490888024e-07	3.00

N	L¹ error	Rate	L^∞ error	Rate
40	1.827054747602715e-04		1.448773504797440e-04
80	2.851024314352313e-05	2.68	1.785661053588239e-05	3.02
160	3.845862448196772e-06	2.89	2.226299234296333e-06	3.00
320	4.929538860536765e-07	2.96	2.782109209450295e-07	3.00
640	6.139221843903657e-08	3.01	3.478015911254420e-08	3.00

High Order Sign Preserving Entropy Stable Schemes

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