Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting

Yang Liu; Huajun Zhu; Zhen-Guo Yan; Feiran Jia; Xinlong Feng

doi:10.3390/e25060911

Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting

Entropy (Basel). 2023 Jun 8;25(6):911. doi: 10.3390/e25060911.

Authors

Yang Liu^{1

2}, Huajun Zhu², Zhen-Guo Yan², Feiran Jia^{2

3}, Xinlong Feng¹

Affiliations

¹ School of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China.
² State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China.
³ School of Power and Energy, Northwestern Polytechnical University, Xi'an 710000, China.

Abstract

The discontinuous Galerkin spectral element method (DGSEM) is a compact and high-order method applicable to complex meshes. However, the aliasing errors in simulating under-resolved vortex flows and non-physical oscillations in simulating shock waves may lead to instability of the DGSEM. In this paper, an entropy-stable DGSEM (ESDGSEM) based on subcell limiting is proposed to improve the non-linear stability of the method. First, we discuss the stability and resolution of the entropy-stable DGSEM based on different solution points. Second, a provably entropy-stable DGSEM based on subcell limiting is established on Legendre-Gauss (LG) solution points. Numerical experiments demonstrate that the ESDGSEM-LG scheme is superior in non-linear stability and resolution, and ESDGSEM-LG with subcell limiting is robust in shock-capturing.

Keywords: Gauss solution points; entropy-stable; high-order methods; shock capturing; subcell limiting.

Grants and funding

This work was supported by the National Numerical Wind Tunnel Project, the National Natural Science Foundation of China (Grant Nos. 12172375, 11902344, 11572342), the Foundation of the State Key Laboratory of Aerodynamics (Grant No. SKLA2019010101), the Natural Science Foundation of China (Grant Nos. 12071406 and U19A2079) and the Natural Science Foundation of Xinjiang Province, China (Grant Nos. 2022TSYCTD0019 and 2022D01D32).