Section: New Results

Relaxation method for Guiding-Center equation

Participants: E. Franck, R. Helie, L. Navoret, P. Helluy.

In previous years, implicit kinetic relaxation methods have been developed to treat conservation laws without CFL and without a non-trivial matrix to reverse [6]-[4]. We have started to apply this method with a spectral discretization for transport equations such as the guiding-center equation (a non constant advection equation coupled with elliptic problem used in plasma physics). The scheme obtained has a very high order of convergence for an instability test case and is very simple to implement. We have also investigated the different kinetic relaxation representations. However, they suffer from inaccuracy at the boundaries. We have proposed a new approach in 1D [8] to analyse this behaviour and a new way to apply boundary conditions to ensure they are compatible both with the approximated system and its kinetic approximation. Extending this approach to higher dimensions is one of the objectives of the thesis of Romane Helie.