Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
---|---|---|
Page(s) | 1107 - 1135 | |
DOI | https://doi.org/10.1051/m2an/2024028 | |
Published online | 26 June 2024 |
High order asymptotic preserving scheme for diffusive scaled linear kinetic equations with general initial conditions
1
Indian Institute of Science, C.V. Raman Road, Bangalore 560012, India
2
Univ Rennes, CNRS, IRMAR UMR 6625, 35000 Rennes, France
3
Univ Rennes, CNRS, IRMAR UMR 6625 & Centre Inria de l’Université de Rennes (MINGuS) & ENS Rennes, Rennes, France
* Corresponding author: benjamin.boutin@univ-rennes.fr
Received:
29
August
2023
Accepted:
13
April
2024
Diffusive scaled linear kinetic equations appear in various applications, and they contain a small parameter ɛ that forces a severe time step restriction for standard explicit schemes. Asymptotic preserving (AP) schemes are those schemes that attain asymptotic consistency and uniform stability for all values of ɛ, with the time step restriction being independent of ɛ. In this work, we develop high order AP scheme for such diffusive scaled kinetic equations with both well-prepared and non-well-prepared initial conditions by employing IMEX-RK time integrators such as CK-ARS and A types. This framework is also extended to a different collision model involving advection-diffusion asymptotics, and the AP property is proved formally. A further extension of our framework to inflow boundaries has been made, and the AP property is verified. The temporal and spatial orders of accuracy of our framework are numerically validated in different regimes of ɛ, for all the models. The qualitative results for diffusion asymptotics, and equilibrium and non-equilibrium inflow boundaries are also presented.
Mathematics Subject Classification: 82C40 / 85A25 / 65M06 / 65L04 / 65L06
Key words: Collisional kinetic equation / diffusive scaling / high order Runge–Kutta schemes / asymptotic preserving property
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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