Stable lattice Boltzmann scheme for a moving Burgers shock wave

François Dubois (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We follow the mathematical framework proposed by Bouchut in 2003 in order to derive equilibrium functions for D1Q3 lattice Boltzmann simulations of the Burgers equation. When a particular convexity property is satisfied, we observe for strong nonlinear shocks and rarefactions that the resulting scheme is numerically stable.

Mots clés: Hyperbolic conservation laws; entropy; convex hull

Domaines: Analyse numérique [math.NA]

François Dubois. Stable lattice Boltzmann scheme for a moving Burgers shock wave. 2010. ⟨hal-00545244v1⟩