Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models (Communications in Computational Physics, 2024)
We elaborate a numerical method for a three-dimensional hydrodynamicmulti-species plasma model described by the Euler-Maxwell equations. Our method isinspired by and extends the one-dimensional scheme from [P. Degond, F. Deluzet, andD. Savelief, Numerical approximation of the Euler-Maxwell model in the quasineutral limit,Journal of Computational Physics, 231 (4), pp. 1917–1946, 2012]. It can cope with largevariations of the Debye length $λ_D$ and is robust in the quasi-neutral limit $λ_D→0$ thanksto its asymptotic-preserving (AP) property. The key ingredients of our approach are (i)a discretization of Maxwell’s equations based on primal and dual meshes in the spiritof discrete exterior calculus (DEC) also known as the finite integration technique (FIT),(ii) a finite volume method (FVM) for the fluid equations on the dual mesh, (iii) mixedimplicit-explicit timestepping, (iv) special no-flux and contact boundary conditions at anouter cut-off boundary, and (v) additional stabilization in the non-conducting regionoutside the plasma domain based on direct enforcement of Gauss’ law. Numericaltests provide strong evidence confirming the AP property of the proposed method.