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

• DOI: 10.1093/mnras/stae1729
• Publication Date: 2024-07-17T22:46:44Z
• Authors: A Mignone; V Berta; M Rossazza; M Bugli; G Mattia; L Del Zanna; L Pareschi
• Keywords: Lorentz force; Robustness

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