Numerical treatment of the nonconservative product in a multiscale fluid model for plasmas in thermal nonequilibrium: application to solar physics

TL;DR

This paper develops a numerical method to accurately simulate shock solutions in multiscale plasma models relevant to solar physics, effectively handling nonconservative products and coarse resolutions.

Contribution

It introduces an original numerical treatment for nonconservative products in plasma models, ensuring physical shock solutions in coarse-resolution simulations.

Findings

The scheme captures traveling wave solutions in high and low resolution cases.

The method avoids non-physical shocks in simplified plasma models.

Numerical results align with physical expectations in solar physics scenarios.

Abstract

This contribution deals with the modeling of collisional multicomponent magnetized plasmas in thermal and chemical nonequilibrium aiming at simulating and predicting magnetic reconnections in the chromosphere of the sun. We focus on the numerical simulation of a simplified fluid model in order to properly investigate the influence on shock solutions of a nonconservative product present in the electron energy equation. Then, we derive jump conditions based on travelling wave solutions and propose an original numerical treatment in order to avoid non-physical shocks for the solution, that remains valid in the case of coarse-resolution simulations. A key element for the numerical scheme proposed is the presence of diffusion in the electron variables, consistent with the physically-sound scaling used in the model developed by Graille et al. following a multiscale Chapman-Enskog expansion method [M3AS, 19 (2009) 527--599]. The numerical strategy is eventually assessed in the framework of a solar physics test case. The computational method is able to capture the travelling wave solutions in both the highly- and coarsely-resolved cases.