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A stable HLLC Riemann solver for relativistic magnetohydrodynamics. (English) Zbl 1349.76618
Summary: In this short note we improve on an HLLC Riemann solver for relativistic magnetohydrodynamics (MHD). The improvement consists in realizing that density jumps as well as jumps in the transverse velocity can be safely incorporated into the HLLC Riemann solver for relativistic MHD. The iteration process described here is low cost, stable and fast-converging. It obviates the need to have one formulation when the longitudinal magnetic field is non-zero and another when it vanishes. Excellent operation is shown on several test problems.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
Software:
RIEMANN; ECHO
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References:
[1] Balsara, D. S., Total variation diminishing scheme for relativistic magnetohydrodynamics, Astrophys. J. Suppl. Ser., 132, 83, (2001)
[2] Balsara, D. S.; Spicer, D. S., A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations, J. Comput. Phys., 149, 270-292, (1999) · Zbl 0936.76051
[3] Balsara, D. S., Multidimensional extension of the HLL Riemann solver; application to Euler and magnetohydrodynamical flows, J. Comput. Phys., 229, 1970-1993, (2010) · Zbl 1303.76140
[4] Balsara, D. S., A two-dimensional HLLC Riemann solver with applications to Euler and MHD flows, J. Comput. Phys., 231, 7476-7503, (2012) · Zbl 1284.76261
[5] Batten, P.; Clarke, N.; Lambert, C.; Causon, D. M., On the choice of wavespeeds for the HLLC Riemann solver, SIAM J. Sci. Comput., 18, 1553-1570, (1997) · Zbl 0992.65088
[6] Gurski, K. F., An HLLC-type approximate Riemann solver for ideal magnetohydrodynamics, SIAM J. Sci. Comput., 25, 2165, (2004) · Zbl 1133.76358
[7] Honkkila, V.; Janhunen, P., HLLC solver for relativistic MHD, J. Comput. Phys., 223, 643-656, (2007) · Zbl 1111.76036
[8] Li, S.-T., An HLLC Riemann solver for magnetohydrodynamics, J. Comput. Phys., 203, 344, (2005) · Zbl 1299.76302
[9] Mignone, A.; Bodo, G., An HLLC Riemann solver for relativistic flows II - magnetohydrodynamics, Mon. Not. R. Astron. Soc., 368, 1040, (2006)
[10] Mignone, A.; Ugliano, M.; Bodo, G., A five-wave HLL Riemann solver for relativistic MHD, Mon. Not. R. Astron. Soc., 393, 1141, (2009)
[11] Miyoshi, T.; Kusano, K., A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics, J. Comput. Phys., 208, 315-344, (2005) · Zbl 1114.76378
[12] Toro, E. F.; Spruce, M.; Speares, W., Restoration of contact surface in the HLL Riemann solver, Shock Waves, 4, 25-34, (1994) · Zbl 0811.76053
[13] Del Zanna, L.; Bucciantini, N.; Londrillo, P., An efficient shock-capturing central-type scheme for multidimensional relativistic flows. II. magnetohydrodynamics, Astron. Astrophys., 400, 397-413, (2003) · Zbl 1222.76122
[14] Del Zanna, L.; Zanotti, O.; Bucciantini, N.; Londrillo, P., ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics, Astron. Astrophys., 473, 11, (2007)
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