| Issue |
ESAIM: M2AN
Volume 56, Number 3, May-June 2022
|
|
|---|---|---|
| Page(s) | 893 - 942 | |
| DOI | https://doi.org/10.1051/m2an/2022022 | |
| Published online | 25 April 2022 | |
Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules
1
Department of Mathematics and Computer Science, University of Catania, 95125 Catania, Italy
2
Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, 52828 Jinju, Republic of Korea
3
Department of Mathematics, Sungkyunkwan University, 440-746 Suwon, Republic of Korea
* Corresponding author: chosy89@skku.edu
Received:
23
April
2021
Accepted:
21
February
2022
In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the convection term with an implicit treatment for the relaxation term. We show how to explicitly solve the implicit step, thus obtaining an efficient and stable scheme for any Knudsen number. We also derive an explicit error estimate on the convergence of the proposed scheme for every fixed value of the Knudsen number.
Mathematics Subject Classification: 35Q20 / 82C40 / 97N40 / 65M12
Key words: Polyatomic ellipsoidal BGK model / Boltzmann equation / semi-Lagrangian scheme / error estimate / kinetic theory of gases
© The authors. Published by EDP Sciences, SMAI 2022
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