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 lattice-kinetic form. A lattice-kinetic 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;

• can be solved by a splitting strategy;

• easy-to-implement implicit schemes, avoiding CFL constraint;

• high parallelism.

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 lattice-kinetic 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 time-integration, viscous terms modeling.