Approximation of mono-dimensional hyperbolic systems: a lattice Boltzmann scheme as a relaxation method

Benjamin Graille (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We focus on mono-dimensional hyperbolic systems approximated by a particular lattice Boltz- mann scheme. The scheme is described in the framework of the multiple relaxation times method and stability conditions are given. An analysis is done to link the scheme with an explicit finite differences approximation of the relaxation method proposed by Jin and Xin. Several numerical illustrations are given for the transport equation, the Burgers equation, the p-system, and the full compressible Euler system.

Mots clés: lattice Boltzmann scheme; relaxation method; hyperbolic system

Domaines: Equations aux dérivées partielles [math.AP]

Benjamin Graille. Approximation of mono-dimensional hyperbolic systems: a lattice Boltzmann scheme as a relaxation method. Journal of Computational Physics, 2014, 266, pp.74-88. ⟨10.1016/j.jcp.2014.02.017⟩. ⟨hal-00919835⟩