A comparison of approximate non-linear Riemann solvers for Relativistic MHD - Mattia, Giancarlo; Mignone, Andrea (Monthly notices of the Royal Astronomical Society, 2022)
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.
Advance Access publication 2021 November 24
Gesehen am 07.10.2022