An IMEX CG/DG approach for the simulation of plasma turbulence
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We will present a finite element approach to solve a subset of the drift reduced Braginskii equations, used to describe plasma turbulence in the boundary of fusion device. The studied system features different phenomena with various time scales: the typical time of interest for turbulence is around 10-5s, while the fastest wave, the shear Alfven wave have a frequency of 108s-1. In order to avoid a drastic CFL condition, we propose to use an IMEX time integration strategy, treating the transport explicitly and the fast wave implicitly. The remaining shear Alfven wave system that needs to be solved implicitly is a constrained system and we exploit this to propose a mixed formulation that can be reduced using a Schur complement method. However, due to the strongly anisotropic nature of the system, this leads to an almost ill posed problem of type A + εB, where A which is a Laplacian along the magnetic field lines is not invertible due to the presence of open field lines. Hence, one must exploit the special structure of the problem to obtain an efficient way to solve it. The aim of this presentation is therefore to present the small Braginskii system, it specific structure and our strategy to obtain a stable and efficient discretization.
