In the paper, we present one design of the HLLC (Harten–Lax–van Leer contact) scheme for solving the equations of special relativistic magnetohydrodynamics. The construction is based on writing equations in the form of a symmetric hyperbolic system and an additional equation for relativistic entropy in order to regularize the numerical solution. To increase the order of accuracy and reduce dissipation at breaks, piecewise parabolic reconstruction of physical variables is used. The developed scheme is verified on the classic one dimensional Alfven test problem and 3D Fireball Blandford–McKee type in a magnetic field test.
Kulikov et al. (Thu,) studied this question.