Section: New Results

High order implicit time splitting schemes for the BGK model

Participants : Michel Mehrenberger, Philippe Helluy, Laurent Navoret, David Coulette, Emmanuel Franck.

In the context of the Lattice Boltzmann or relaxation methods (6.1-6.3), it is interesting to obtain a very high order implicit splitting. For this, we have considered a time splitting discretization of the BGK model with 3 velocities. First and second order schemes are studied before using Strang splitting coupled with a Semi Lagrangian or a Cranck-Nicholson DG scheme. Using complex time steps and composition methods, we obtain 4th order time step, unconditionally stable for the discrete BGK models. These results could be used with the Lattice Boltzmann method, the relaxation method and also the kinetic model.