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Section: New Results

MHD problems

Participant : Emmanuel Franck.

Compatible Implicit finite element for linear MHD

In this work we consider a linear MHD problem. The aim is to design an implicit method able to preserve the energy equation and the divergence free constraints in realistic Tokamak geometry. The first idea is to use a splitting scheme between the wave and convection parts coupled with an implicit scheme for each subsystem. In order to discretize each sub-system we use compatible B-Splines FE method wich allows us to preserve the invariants and to use a reduction of the implicit problem to be inverted. The idea was improved on simple geometries. We are currently extending the method on realistic geometries.

Splitting and relaxation for JOREK code

The Jorek code is the main European code for the simulation of Tokamak instabilities. The inversion of the full matrix is based on Block Jacobi preconditioning which is not efficient in some cases and very greedy in memory. We are investigating a new splitting scheme similar to the one used in works on compatible Finite Elements. We have also just begun to investigate the relaxation method used in the Palindromic scheme to solve the reduced MHD model of JOREK.