Stability analysis of an implicit lattice Boltzmann scheme

Philippe Helluy (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 TONUS - TOkamaks and NUmerical Simulations

We analyze the D1Q3 lattice kinetic model, which is the simplest kinetic model representing the isothermal Euler equations. We show that it is entropy unstable but that it can be made stable if the transport step is solved with an implicit numerical scheme.

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Helluy. Stability analysis of an implicit lattice Boltzmann scheme. Colombo, Rinaldo; Lefloch, Philippe; Rohde, Christian. Hyperbolic Techniques in Modelling, Analysis and Numerics., 13, pp.1710-1715, 2016, Oberwolfach Reports. ⟨hal-01403759⟩