Beyond ideal MHD: towards a more realistic modeling of relativistic astrophysical plasmas

TL;DR

This paper introduces a new numerical method using IMEX Runge Kutta techniques for more realistic modeling of relativistic astrophysical plasmas, especially where resistive effects are significant and vary widely.

Contribution

The authors develop a novel implicit-explicit Runge Kutta approach for solving relativistic resistive MHD equations, enabling unified treatment of different plasma regimes.

Findings

The method accurately captures resistive effects across diverse conditions.

It demonstrates robustness compared to traditional splitting techniques.

The approach effectively models both fluid-pressure and magnetic-pressure dominated regions.

Abstract

Many astrophysical processes involving magnetic fields and quasi-stationary processes are well described when assuming the fluid as a perfect conductor. For these systems, the ideal-magnetohydrodynamics (MHD) description captures the dynamics effectively and a number of well-tested techniques exist for its numerical solution. Yet, there are several astrophysical processes involving magnetic fields which are highly dynamical and for which resistive effects can play an important role. The numerical modeling of such non-ideal MHD flows is significantly more challenging as the resistivity is expected to change of several orders of magnitude across the flow and the equations are then either of hyperbolic-parabolic nature or hyperbolic with stiff terms. We here present a novel approach for the solution of these relativistic resistive MHD equations exploiting the properties of implicit-explicit (IMEX) Runge Kutta methods. By examining a number of tests we illustrate the accuracy of our approach under a variety of conditions and highlight its robustness when compared with alternative methods, such as the Strang-splitting. Most importantly, we show that our approach allows one to treat, within a unified framework, both those regions of the flow which are fluid-pressure dominated (such as in the interior of compact objects) and those which are instead magnetic-pressure dominated (such as in their magnetospheres)