A fourth-order accurate finite volume scheme for resistive relativistic MHD

We present a finite-volume, genuinely fourth-order accurate numerical method for solving the equations of resistive relativistic magnetohydrodynamics in Cartesian coordinates. In our formulation, the magnetic field is evolved in time in terms of face-average values via the constrained-transport method, while the remaining variables (density, momentum, energy, and electric fields) are advanced as cell volume averages. Spatial accuracy employs fifth-order accurate WENO-Z reconstruction from point values (as described in a companion paper) to obtain left and right states at zone interfaces. Explicit flux evaluation is carried out by solving a Riemann problem at cell interfaces, using the Maxwell–Harten–Lax–van Leer with contact wave resolution. Time-stepping is based on the implicit–explicit Runge–Kutta (RK) methods, of which we consider both the third-order strong stability preserving SSP3(4,3,3) and a recent fourth-order additive RK scheme, to cope with the stiffness introduced by the source term in Ampere’s law. Numerical benchmarks are presented in order to assess the accuracy and robustness of our implementation.