Section: New Results
Implicit Lattice Boltzmann scheme for fluid models
Participants : Emmanuel Franck, Philippe Helluy, David Coulette, Conrad Hillairet.
Many systems of conservation laws can be written under a latticekinetic form. A latticekinetic model is made of a finite set of transport equations coupled through a relaxation source term. Such representation is very useful:

easy stability analysis, possibility to add second order terms in a natural way;

easytoimplement implicit schemes, avoiding CFL constraint;
We have started to work on such approaches for solving the MHD equation inside a tokamak (postdoc of David Coulette). We have programmed a generic parallel latticekinetic solver in Kirsch, using the StarPU runtime. It presents a very good parallel efficiency. We have also started studying more theoretical aspects: stability of kinetic models, higher order timeintegration, viscous terms modeling.