High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms

Wang，Jiangfu1; Tang，Huazhong1,2; Wu，Kailiang3

2024-12-15

10.1016/j.jcp.2024.113451

Journal of Computational Physics   影响因子和分区

0021-9991

1090-2716

This paper proposes novel high-order accurate discontinuous Galerkin (DG) schemes for the one- and two-dimensional ten-moment Gaussian closure equations with source terms defined by a known potential function. Our DG schemes exhibit the desirable capability of being well-balanced (WB) for a known hydrostatic equilibrium state while simultaneously preserving positive density and positive-definite anisotropic pressure tensor. The well-balancedness is built on carefully modifying the solution states in the Harten–Lax–van Leer–contact (HLLC) flux, and appropriate reformulation and discretization of the source terms. Our novel modification technique overcomes the difficulties posed by the anisotropic effects, maintains the high-order accuracy, and ensures that the modified solution state remains within the physically admissible state set. We provide the rigorous positivity-preserving analyses of our WB DG schemes, based on several key properties of the admissible state set, the HLLC flux and the HLLC solver, as well as the geometric quasilinearization (GQL) approach in Wu and Shu (2023) [52], which was originally applied to analyze the admissible state set and the physical-constraints-preserving schemes for the relativistic magnetohydrodynamic equations in Wu and Tang (2017) [54], to address the difficulties arising from the nonlinear constraints on the pressure tensor. Moreover, the proposed WB DG schemes satisfy the weak positivity for the cell averages, implying the use of a simple scaling limiter to enforce the physical admissibility of the DG solution polynomials at certain points of interest. Extensive numerical experiments are conducted to validate the preservation of equilibrium states, accuracy in capturing small perturbations to such states, robustness in solving problems involving low density or low pressure, and high resolution for both smooth and discontinuous solutions.

Anisotropic pressure tensor Discontinuous Galerkin schemes Geometric quasilinearization (GQL) Positivity-preserving Ten-moment Gaussian closure equations Well-balanced

英语

通讯

2-s2.0-85204707346

Scopus

1.Center for Applied Physics and Technology,HEDPS,LMAM,School of Mathematical Sciences,Peking University,Beijing,100871,China
2.Nanchang Hangkong University,Nanchang,Jiangxi Province,330000,China
3.Department of Mathematics,Shenzhen International Center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Wang，Jiangfu,Tang，Huazhong,Wu，Kailiang. High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms[J]. Journal of Computational Physics,2024,519.

Wang，Jiangfu,Tang，Huazhong,&Wu，Kailiang.(2024).High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms.Journal of Computational Physics,519.

Wang，Jiangfu,et al."High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms".Journal of Computational Physics 519(2024).