Dissipative Magnetohydrodynamics for Non-Resistive Relativistic Plasmas

TL;DR

This paper introduces a new numerical scheme for relativistic dissipative magnetohydrodynamics based on a 14-moment closure, capable of handling all first-order dissipative effects and magnetic anisotropies, suitable for turbulent flow simulations.

Contribution

It presents a novel flux-divergence form formulation and numerical implementation for relativistic dissipative MHD with magnetic anisotropies, bridging collisional and collisionless plasma regimes.

Findings

Successfully tests the numerical scheme in flat spacetime.

Captures thermal Hall effect and magnetic anisotropies.

Interpolates between neutron star and black hole plasma regimes.

Abstract

Based on a 14-moment closure for non-resistive (general-) relativistic viscous plasmas, we describe a new numerical scheme that is able to handle all first-order dissipative effects (heat conduction, bulk and shear viscosities), as well the anisotropies induced by the presence of magnetic fields. The latter is parameterized in terms of a thermal gyrofrequency or, equivalently, a thermal Larmor radius and allows to correctly capture the thermal Hall effect. By solving an extended Israel-Stewart-like system for the dissipative quantities that enforces algebraic constraints via stiff-relaxation, we are able to cast all first-order dissipative terms in flux-divergence form. This allows us to apply traditional high-resolution shock capturing methods to the equations, making the system suitable for the numerical study of highly turbulent flows. We present several numerical tests to assess the robustness of our numerical scheme in flat spacetime. The 14-moment closure can seamlessly interpolate between the highly collisional limit found in neutron star mergers, and the highly anisotropic limit of relativistic Braginskii magnetohydrodynamics appropriate for weakly collisional plasmas in black-hole accretion problems. We believe that this new formulation and numerical scheme will be useful for a broad class of relativistic magnetized flows.