Section: New Results

Numerical methods for Euler/MHD models

Splitting scheme in JOREK code

Participants: Emmanuel Franck

The Jorek code is the main European code for the simulation of Tokamak instabilities. The inversion of the full matrix is based on a Block Jacobi preconditioning which is not efficient in some cases and very greedy in memory. To solve the problem we investigate on splitting scheme which will allow to solve some simple subsystems separately. The splitting scheme have been tested on the first MHD model on JOREK in the quasi-linear case. In this regime the splitting gives good results since the accuracy is close to the original full implicit solver. The nonlinear case is currently studied.

Compatible finite element for MHD

Participants: Emmanuel Franck, Eric Sonnendruecker (IPP), Mustaga Gaja (iPP)

The works on the compatible finite elements for MHD is continued. This method allows to preserve the energy balance or the divergence free constrains with high-order finite element on complex geometries. This method is coupled with a splitting between the different physical parts and a nonlinear solver. The method gives expected results for Maxwell and Acoustic and also gives good results for the nonlinear acoustic part of the MHD model. The magnetic and convective parts of the MHD model are currently studied.

Semi implicit for relaxation model in low-Mach regime

Participants: Emmanuel Franck, Laurent Navoret.

To apply the previous method, we must invert a nonlinear problem. A parabolization method allows to reduce the dimension of the implicit problem. However the problem is still nonlinear and ill-conditioned for strong gradient of the physical quantities. To avoid this, we propose a new relaxation method for the Euler equations (to begin) which allows to linearize the acoustic part preserving the low-Mach limit (which is the relevant regime for our application). This relaxation method allows to obtain a well-conditioned and linear implicit part. The method is validated in 1D/2D in a finite volumes context and will be extended to the high-order scheme and MHD model.