HLLC solver for ideal relativistic MHD. (English) Zbl 1111.76036

Summary: We develop an approximate Riemann solver of Godunov type for ideal relativistic magnetohydrodynamic equations named as HLLC (“C” denotes contact). In HLLC the Riemann fan is approximated by two intermediate states, which are separated by entropy wave. Numerical tests show that HLLC resolves contact discontinuity more accurately than the Harten-Lax-van Leer (HLL) method, and resolves an isolated contact discontinuity exactly.


76M12 Finite volume methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics


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[1] Anile, A.M., Relativistic fluids and magneto-fluids, (1989), Cambridge University Press Cambridge · Zbl 0701.76003
[2] Balsara, D.S., Total variation diminishing scheme for relativistic magnetohydrodynamics, Apjs, 132, 83, (2001)
[3] Batten, P.; Clarke, N.; Lambert, C.; Causon, D.M., On the choice of wave speeds for the HLLC Riemann solver, SIAM J. sci. stat. comp., 35, 1553, (1997) · Zbl 0992.65088
[4] Davis, S.F., Simplified second-order Godunov-type methods, SIAM J. sci. statist. comput., 9, 445, (1988) · Zbl 0645.65050
[5] Del Zanna, L.; Bucciantini, N., An efficient shock-capturing central-type scheme for multidimensional relativistic flows, A&a, 390, 1177, (2002) · Zbl 1209.76022
[6] Gurski, K.F., An HLLC-type approximate Riemann solver for ideal magnetohydrodynamics, SIAM J. sci. comp., 25, 2165, (2004) · Zbl 1133.76358
[7] Harten, A.; Lax, P.D.; van Leer, B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM rev., 25, 35, (1983) · Zbl 0565.65051
[8] Koldoba, A.V.; Kuznetsov, O.A.; Ustyugova, G.V., An approximate Riemann solver for relativistic magnetohydrodynamics, Mon. not. R. astron. soc., 333, 932, (2002)
[9] Lichnerowicz, A., Relativistic hydrodynamics and magnetohydrodynamics, (1967), Benjamin Press New York · Zbl 0193.55401
[10] LeVeque, R.J., Nonlinear conservation laws and finite volume methods for astrophysical fluid flow, Computational methods for astrophysical fluid flow, (1998), Springer Verlag
[11] Li, S., An HLLC Riemann solver for magneto-hydrodynamics, J. comp. phys., 203, 344, (2005) · Zbl 1299.76302
[12] Meier, D.L.; Koide, S.; Uchida, Y., Magnetohydrodynamic production of relativistic jets, Science, 291, 84, (2001)
[13] Mignone, A.; Bodo, G., An HLLC solver for relativistic flows-I. hydrodynamics, Mon. not. R. astron. soc., 364, 126, (2005)
[14] Mignone, A.; Bodo, G., An HLLC solver for relativistic flows-II. magnetohydrodynamics, Mon. not. R. astron. soc., 368, 1040, (2006)
[15] Miyoshi, T.; Kusano, K., A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics, J. comp. phys., 208, 315, (2005) · Zbl 1114.76378
[16] Toro, E.F.; Spruce, M.; Speares, W., Restoration of the contact surface in the HLL Riemann solver, Shock waves, 4, 25, (1994) · Zbl 0811.76053
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