A nonlocal electron transport model in the diffusion scaling of hydrodynamics

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.

Automated summary

In this paper, a model of nonlocal electron transport called P1-diffusion is analyzed. It is 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 and asymptotic preserving discretization method is proposed, which requires inversion of a potentially large number of but small linear systems. The accuracy of this approach is validated by comparing with reference solutions from a Vlasov-Fokker-Planck-Maxwell code on a series of tests, representing the conduction zone in laser-created plasmas. Therefore, this method is a good candidate for integration into multi-D MHD codes.