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Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models

Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models

Year:    2024

Author:    Tianwei Yu, Roman Fuchs, Ralf Hiptmair

Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 581–617

Abstract

We elaborate a numerical method for a three-dimensional hydrodynamic multi-species plasma model described by the Euler-Maxwell equations. Our method is inspired by and extends the one-dimensional scheme from [P. Degond, F. Deluzet, and D. 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 large variations of the Debye length $λ_D$ and is robust in the quasi-neutral limit $λ_D→0$ thanks to 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 spirit of 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) mixed implicit-explicit timestepping, (iv) special no-flux and contact boundary conditions at an outer cut-off boundary, and (v) additional 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 proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0270

Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 581–617

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    37

Keywords:    Asymptotic-preserving scheme finite integration technique Maxwell-Euler equations.

Author Details

Tianwei Yu

Roman Fuchs

Ralf Hiptmair