## 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 [37] . 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.

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 (`RealfluiDS ` ).

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 initialization phase, in order to guarantee the equilibrium, then we will apply the modifications on the mesh in order to get the adaptative mesh refinement procedure during the whole simulation.

The `JOREK` code is now able to use several hundred of processors routinely. Simulations of ELMs
are produced taking into account the X-point geometry with both closed and open field lines. But a
higher toroidal resolution is required for the resolution of the fine scale filaments that form during
the ELM instability. The complexity of the tokamak's geometry and the fine mesh that is required
leads to prohibitive memory requirements. In the current release, the memory scaling is not
satisfactory: as one increases the number of processes for a given problem size, the memory
footprint on each process does not reduce as much as one can expect.
This will be one of the goals that motivate the partners involved in this project to present a new collaboration proposal.