Section: New Results

Time scheme for finite elements code for fluids models

Participants : Emmanuel Franck, Philippe Helluy, David Coulette, Ahmed Ratnani, Eric Sonnendrücker.

The finite element code JOREK use currently a classical implicit solver for reduced MHD model coupled with a block Jacobi preconditioning. For the future full MHD code we propose to change the solver in time to reduce the memory consumption and improve the robustness. During this year two directions have been followed. The first one is based on the classical physics-based preconditioning proposed by L. Chacon. Firstly, we have generalized this method by rewriting the preconditioning as a splitting scheme which separates the advection terms and the acoustic part and by generalizing the splitting algorithm. We obtain different solutions with different advantages. These different splitting schemes have been tested on simplified models and are currently tested on the Euler equations. The second direction is to use a relaxation scheme which allows to rewrite a nonlinear system as a linear hyperbolic system (larger that the previous one) and a nonlinear local source term. Using a splitting scheme we obtain a very simple method where in the first step we solve independent linear transport problems and in a second step we have some nonlinear projections. With a good parallelism and good solver for the transport subproblems the algorithm is very efficient compared to the classical one.