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

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 to investigate the influence on shock solutions of a nonconservative product present in the electron energy equation. Then, we derive jump conditions based on traveling wave solutions and propose an original numerical treatment in order to avoid nonphysical 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, Magin, and Massot following a multiscale Chapman-Enskog expansion method [Math. Models Methods Appl. Sci., 19 (2009), pp. 527-599]. The numerical strategy is assessed in the framework of a solar physics test case. The computational method is able to capture the traveling wave solutions in both the highly- and coarsely resolved cases.