## Section: New Results

### High performance simulation for plasma physics

Participants : Rémi Abgrall, Robin Huart, Pascal Hénon, Pierre Ramet [ Corresponding member ] , Hocine Sellama.

We have been involved in two tasks : in the first one we work on novel numerical schemes for solving the compressible resistive MHD equations. In the second one, in connecting with the JOREK code developped in CEA Cadarache, we work on adaptive mesh refinement problems and their connection with the solution of large linear systems to be solved in parallel. This has led to two publications [14] , [21] .

The aim of our work in the ASTER project is to provide an efficient numerical method for solving the MHD equations, more especially in the form they are used for the ITER model. Here we want to improve the ability of Residual Distribution schemes to solve this hyperbolic system.
Once fixed the choice of the full set of equations and the behavior of physical parameters, and with a validated numerical solver for these equations, we should be able to simulate plasma instabilities like those encountered in the ITER tokamak configuration. The step to ELMs simulations would then be achieved. This is a global view of the context, and it may be seen as a framework. However, one should notice that, contrarily to the work on JOREK at the CEA Cadarache, our purpose is a more general and academic code (`FluidBox` ).

Due to the localized nature of the ELMs at the boundary of the plasma the use of mesh refinement is ideally suited to minimize the number of elements required for a given accuracy. The high resolution is only required where large gradients develop which is on a surface which is deforming in time. At a later stage during the ELM evolution, blobs of plasma are disconnected from the main plasma for which a mesh refinement also appears to be an optimal solution. We first adapt the mesh at the beginning of the simulation during the initialisation phase, in order to garanty the equilibrium, then we will apply the modifications on the mesh in order to get the adaptative mesh refinement procedure during the whole simulation.