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Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models

by T. Yu and R. Fuchs and R. Hiptmair

(Report number 2023-15)

Abstract
We elaborate a numerical method for a three-dimensional hydrodynamic multi-species plasma model which boils down to an extended Euler-Maxwell system. Our method is inspired by and extends the one-dimensional scheme from \([\)P.~Degond, F.~Deluzet, and D.~Savelief, \emph{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 large variations of the so-called Debye length \(\lambda_D\) and is robust in the quasi-neutral singular-perturbation limit \(\lambda_D\to 0\), because it enjoys an \emph{asymptotic-preserving} (AP) property in the sense that in the sense that the limit \(\lambda_D\to 0\) of the scheme yields a viable discretization for the continuous limit model. The key ingredients of our approach are (i) a discretization of Maxwell's equations based on primal and dual meshes in the spirit of \emph{discrete exterior calculus} (DEC) also known the finite integration technique (FIT), (ii) a finite volume method (FVM) for the fluid equations on the dual mesh, (iii) \emph{mixed implicit-explicit timestepping}, (iv) special no-flux and contact boundary conditions at an outer cut-off boundary, and (v) additional \emph{stabilization} in the non-conducting region outside the plasma domain based on direct enforcement of Gauss' law. Numerical tests provide strong evidence confirming the AP property of the new method.

Keywords: Plasma fluid models, Asymptotic-preserving schemes, Quasi-neutrality, Finite Integration Technique, Primal-dual meshes, Lagrange multiplier,

@Techreport{YFH23_1052,
  author = {T. Yu and R. Fuchs and R. Hiptmair},
  title = {Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-15.pdf },
  year = {2023}
}

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