A nonlocal electron transport model in the diffusion scaling of hydrodynamics

Abstract

We analyze a model of nonlocal electron transport named P1-diffusion based on a spherical harmonic expansion in velocity space and a diffusion scaling, which makes it compatible with assumptions from magneto-hydrodynamics (MHD). An iterative, fully implicit (CFL-free, as defined by the Courant Friedrich Levy condition) and asymptotic preserving discretization is proposed, which necessitates the inversion of a possibly large number of—but small—linear systems. It is found accurate with respect to reference solutions from a Vlasov–Fokker–Planck–Maxwell code (based on a Polynomial expansion of order N, or PN expansion) on a series of tests, which are representative of the conduction zone in laser-created plasmas. Thereby, the present approach is a good candidate for being embedded in multi-D MHD codes.