Bienvenue - Laboratoire Jacques-Louis Lions

Mardi 9 Avril 2019 à 14h : Alejandro Alvarez Laguna (CMAP, Ecole Polytechnique)

(attention, horaire inhabituel)

An asymptotic preserving well-balanced scheme for the isothermal fluid plasma equations in low-temperature plasma applications

We present a novel numerical scheme for the efficient and accurate resolution of the moment equations for low-temperature plasmas coupled to Poisson’s equation. The model considers electrons and ions as separate fluids, comprising the electron inertia and a finite Debye length. The discretization of this system with standard explicit schemes is constrained to the resolution of the Debye length, the electron plasma frequency, and the electron sound waves. In this work we discuss the asymptotic behaviour of the set of equations with respect to two parameters : the electron-to-ion mass ratio and the Debye length. The proposed scheme is based on the Lagrange-projection operator splitting and it preserves the asymptotic regime where the plasma is quasi-neutral with massless electrons. A well-balance treatment of the ion source terms is proposed in order to tackle problems where the ion temperature is very low compared to this of electrons. The scheme proves to significantly improve the accuracy both in the quasi-neutral limit and in the presence of plasma sheaths. As a result, the computational time of the simulation is dramatically reduced by several orders of magnitude when the plasma is quasi-neutral as compared to a standard discretization that needs to resolve the small scales.