no. 3
Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 893-942

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.

DOI : 10.1051/m2an/2022022
Classification : 35Q20, 82C40, 97N40, 65M12
Keywords: Polyatomic ellipsoidal BGK model, Boltzmann equation, semi-Lagrangian scheme, error estimate, kinetic theory of gases 
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     title = {Convergence estimates of a {semi-Lagrangian} scheme for the ellipsoidal {BGK} model for polyatomic molecules},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {893--942},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
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Boscarino, Sebastiano; Cho, Seung Yeon; Russo, Giovanni; Yun, Seok-Bae. Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 893-942. doi: 10.1051/m2an/2022022

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