Workshop on Numerical Methods and Analysis in CFD - Abstract
Yu, Tianwei
A key coefficient characterizing plasmas is the so-called Debye length λD, whose size indicates to what extent electric charges can deviate from the neutral case: If λD = O(1) we face the non-neutral regime, while for λD → 0 the plasma becomes quasi-neutral. Plasma models have rather different properties in these two regimes due to the singular perturbation arising from the λD → 0 limit. Since both regimes may coexist in some plasma phenomena, it is desired to design numerical schemes that are emphrobust for arbitrary λD. More precisely, they should be emphasymptotic-preserving (AP), in the sense that the limit λD → 0 of the scheme yields a viable discretization for the continuous limit model.
An asymptotic preserving scheme for single- and multi-fluid Euler-Maxwell system was proposed in [1] for one spatial dimension. We start from their dimensionless model and extend the scheme to three dimensions. The key ingredients are
(i) a discretization of Maxwell's equations based on primal and dual meshes in the spirit of discrete exterior calculus (DEC)/the finite integration technique (FIT),
(ii) finite volume method (FVM) for the fluid equations on the dual mesh, and
(iii) mixed implicit-explicit timestepping.
This scheme turns out to be AP for λD → 0 both in terms of structure and empirically in numerical test. Special care is necessary for the boundary conditions which must be valid in both regimes. Additionally, if the electromagnetic fields have to be modeled in an insulating region beyond the plasma domain, additional stabilization is necessary to accommodate Gauss's law.
References:
[1] Degond, P., Deluzet, F., and Savelief, D., Numerical approximation of the Euler-Maxwell model in the quasineutral limit. emphJournal of Computational Physics, 231(4):1917--1946, 2012.