A New numerical scheme for resistive relativistic MHD using method of characteristics

TL;DR

This paper introduces a novel numerical scheme for resistive relativistic MHD that accurately handles a wide range of phenomena, including nonrelativistic and relativistic shocks, discontinuities, and waves, especially in systems with weak magnetic fields.

Contribution

The paper presents a new numerical method combining an approximate Riemann solver with the method of characteristics for electromagnetic fields, capable of accurately simulating resistive relativistic MHD phenomena.

Findings

Successfully simulates nonrelativistic to relativistic MHD phenomena.

Accurately captures shocks, discontinuities, and Alfvén waves.

Effective in systems with weak magnetic fields and mixed velocities.

Abstract

We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from nonrelativistic to relativistic (shock, contact discontinuity, and Alfv\'en wave). The present scheme calculates the numerical flux of fluid by using an approximate Riemann solver, and electromagnetic field by using the method of characteristics. Since this scheme uses appropriate characteristic velocities, it is capable of accurately solving problems that cannot be approximated as ideal magnetohydrodynamics and whose characteristic velocity is much lower than light velocity. The numerical results show that our scheme can solve the above problems as well as nearly ideal MHD problems. Our new scheme is particularly well suited to systems with initially weak magnetic field, and mixed phenomena of relativistic and non-relativistic velocity; for example, MRI in accretion disk, and super Alfv\'enic turbulence.