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 - <p style="text-align: justify;">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.</p>