A comparison of approximate non-linear Riemann solvers for Relativistic MHD. (arXiv:2111.09369v2 [astro-ph.HE] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Mattia_G/0/1/0/all/0/1">Giancarlo Mattia</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mignone_A/0/1/0/all/0/1">Andrea Mignone</a>
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 multi-dimensional 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.
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 multi-dimensional 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.
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