A comparison of approximate non-linear Riemann solvers for Relativistic MHD

被引:4
|
作者
Mattia, G. [1 ,2 ]
Mignone, A. [3 ,4 ]
机构
[1] Heidelberg Univ, Max Planck Inst Astron, Konigstuhl 17, D-69117 Heidelberg, Germany
[2] Heidelberg Univ, IMPRS, Konigstuhl 17, D-69117 Heidelberg, Germany
[3] Univ Torino, Dipartimento Fis, Via P Giuria 1, I-10125 Turin, Italy
[4] INAF, Osservatorio Astron Torino, Str Osservatorio 20, I-10025 Pino Torinese, Italy
关键词
MHD; relativistic processes; shock waves; methods: numerical; GODUNOV-TYPE METHODS; CENTRAL-TYPE SCHEME; MAGNETOHYDRODYNAMICS; FLOWS; WAVES; CODE;
D O I
10.1093/mnras/stab3373
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We compare a particular selection of approximate solutions of the Riemann problem in the context of ideal relativistic magnetohydrodynamics. In particular, we focus on Riemann solvers not requiring a full eigenvector structure. Such solvers recover the solution of the Riemann problem by solving a simplified or reduced set of jump conditions, whose level of complexity depends on the intermediate modes that are included. Five different approaches - namely the HLL, HLLC, HLLD, HLLEM, and GFORCE schemes - are compared in terms of accuracy and robustness against one - and multidimensional standard numerical benchmarks. Our results demonstrate that - for weak or moderate magnetizations - the HLLD Riemann solver yields the most accurate results, followed by HLLC solver(s). The GFORCE approach provides a valid alternative to the HLL solver being less dissipative and equally robust for strongly magnetized environments. Finally, our tests show that the HLLEM Riemann solver is not cost-effective in improving the accuracy of the solution and reducing the numerical dissipation.
引用
收藏
页码:481 / 499
页数:19
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