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Volume 36, Issue 3
Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models

Tianwei Yu, Roman Fuchs & Ralf Hiptmair

Commun. Comput. Phys., 36 (2024), pp. 581-617.

Published online: 2024-10

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  • 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.

  • AMS Subject Headings

65M15, 65N08, 76X05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-36-581, author = {Yu , TianweiFuchs , Roman and Hiptmair , Ralf}, title = {Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models}, journal = {Communications in Computational Physics}, year = {2024}, volume = {36}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0270}, url = {http://global-sci.org/intro/article_detail/cicp/23453.html} }
TY - JOUR T1 - Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models AU - Yu , Tianwei AU - Fuchs , Roman AU - Hiptmair , Ralf JO - Communications in Computational Physics VL - 3 SP - 581 EP - 617 PY - 2024 DA - 2024/10 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2023-0270 UR - https://global-sci.org/intro/article_detail/cicp/23453.html KW - Asymptotic-preserving scheme, finite integration technique, Maxwell-Euler equations. AB -

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.

Yu , TianweiFuchs , Roman and Hiptmair , Ralf. (2024). Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models. Communications in Computational Physics. 36 (3). 581-617. doi:10.4208/cicp.OA-2023-0270
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