Geodesic
Stability analysis of the vectorial Lattice-Boltzmann method
Kévin Guillon1 ; Romane Hélie1, 2 ; Philippe Helluy2
1 Institut de Mathématiques de Bordeaux, CNRS, UMR 5251, Bordeaux, France
2 Université de Strasbourg, CNRS, IRMA UMR 7501, Inria Tonus, Strasbourg, France
ESAIM. Proceedings, Tome 77 (2024), pp. 46-78.

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We perform a stability analysis of the Vectorial Lattice-Boltzmann Method (VLBM). The VLBM has been introduced in [1–3, 9, 18]. It is a variant of the LBM with extended stability features: it allows handling compressible flows with shock waves, while the LBM is limited to low-Mach number regime. The stability analysis is based on the Legendre transform theory. We also propose a new tool: the equivalent system analysis, which we conjecture to contains both the stability and the consistency of the VLBM.
DOI : 10.1051/proc/202477046

Kévin Guillon 1 ; Romane Hélie 1, 2 ; Philippe Helluy 2

1 Institut de Mathématiques de Bordeaux, CNRS, UMR 5251, Bordeaux, France
2 Université de Strasbourg, CNRS, IRMA UMR 7501, Inria Tonus, Strasbourg, France 
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Kévin Guillon; Romane Hélie; Philippe Helluy. Stability analysis of the vectorial Lattice-Boltzmann method. ESAIM. Proceedings, Tome 77 (2024), pp. 46-78. doi : 10.1051/proc/202477046. https://geodesic-test.mathdoc.fr/articles/10.1051/proc/202477046/

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