An Admissible Asymptotic-Preserving Numerical Scheme for the Electronic $M_1$ Model in the Diffusive Limit

Abstract

This work is devoted to the derivation of an admissible asymptotic-preserving scheme for the electronic $M_1$ model in the diffusive regime. A numerical scheme is proposed in order to deal with the mixed derivatives which arise in the diffusive limit leading to an anisotropic diffusion. The derived numerical scheme preserves the realisability domain and enjoys asymptotic-preserving properties correctly handling the diffusive limit recovering the relevant limit equation. In addition, the cases of non constants electric field and collisional parameter are naturally taken into account with the present approach. Numerical test cases validate the considered scheme in the non-collisional and diffusive limits.