Multidimensional Hall magnetohydrodynamics with isotropic or anisotropic thermal pressure: numerical scheme and its validation using solitary waves

TL;DR

This paper introduces a numerical solver for Hall magnetohydrodynamics that handles isotropic and anisotropic thermal pressures, validated through standard tests and a novel solitary wave method for nonlinear regime accuracy.

Contribution

The paper presents a new numerical scheme for multidimensional HMHD with thermal pressure anisotropy, including a novel solitary wave validation method for nonlinear testing.

Findings

The solver accurately reproduces known test problems.

The solitary wave validation method effectively tests nonlinear regimes.

The scheme conserves magnetic divergence and energy with high fidelity.

Abstract

We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of accuracy and performance of the implemented code show the fidelity of the proposed approach.