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

ABSTRACT We compare a particular selection of approximate solutions the Riemann problem in context ideal relativistic magnetohydrodynamics. In particular, we focus on solvers not requiring full eigenvector structure. Such recover solution by solving simplified or reduced set jump conditions, whose level complexity depends intermediate modes that are included. Five different approaches – namely HLL, HLLC, HLLD, HLLEM, and GFORCE schemes compared terms accuracy robustness against one multidimensional standard numerical benchmarks. Our results demonstrate for weak moderate magnetizations HLLD solver yields most accurate results, followed HLLC solver(s). The approach provides valid alternative to HLL being less dissipative equally robust strongly magnetized environments. Finally, our tests show HLLEM is cost-effective improving reducing dissipation.