We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics (RRMHD) that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through one-and two-dimensional test problems.

Abstract. Including resistive effects in relativistic magnetized plasmas is a challenging task, that a number of authors have recently tackled employing different methods. From the numerical point of view, the difficulty in including non-ideal terms arises from the fact that, in the limit of very high plasma conductivity (i.e., close to the ideal MHD limit), the system of governing equations becomes stiff, and the standard explicit integrating methods produce instabilities that destroy the numerical solution. To deal with such a difficulty, we have extended the relativistic MHD code MR-GENESIS, to include a number of Implicit Explicit Runge-Kutta (IMEX-RK) numerical methods. To validate the implementation of the IMEX-RK schemes, two standard tests are presented in one and two spatial dimensions, covering different conductivity regimes.