Section: New Results

Palindromic methods

Palindromic discontinuous Galerkin method in 2D and 3D

Participants : David Coulette, Florence Drui, Emmanuel Franck, Philippe Helluy, Laurent Navoret.

In the previous year (see [7]) we have proposed a method to solve hyperbolic systems like the Euler equations with an unconditionally stable high-order method. This method is based on a kinetic representation of the hyperbolic system. The kinetic equations are solved with an upwind DG method. It requires no matrix storage. High order is obtained through palindromic composition methods. The concept has been test in 1D. During this year we extend the method to 2D and 3D and applied it to fluid mechanics. Currently we are working on improving this method on realistic cases for MHD instabilities. The objective is to compare the results with the European code JOREK.

We are also working on methods for applying boundary conditions in a stable way with the palindromic method (postdoc of Florence Drui).

Kinetic model for palindromic methods

Participants : David Coulette, Emmanuel Franck, Laurent Navoret.

One of the most important drawbacks of the Palindromic method is the numerical dispersion associated to the high-order time scheme. To limit this problem we propose to replace the DG method by a semi-Lagrangian method and design new kinetic representations which are more accurate. We also studied the stability of these news models. The first results were good and currently we are working on the 2D extension and the coupling with limiter technics.

Finite element relaxation methods for fluid models

Participants : David Coulette, Emmanuel Franck.

In parallel to our work on the Palindromic method based on a kinetic relaxation model, we studied in [17] a variant based on the Xin-Jin relaxation model. Coupled with a finite element method we obtain an implicit solver for Euler equations where we invert only Laplacians and mass matrices. The first results show that the method is more efficient in CPU costs and memory. The finite elements used are the same as in JOREK.