Section: New Results

Development of a full MHD Modeling

Participants : José Costa, Jeaniffer Vides, Boniface Nkonga.

The single fluid full MHD numerical model has been developed. The divergence free constraint on the magnetic field is achieved by introduction of a potential vector. The use of the potential vector has the additional advantage that the toroidal component is the magnetic flux of the Grad-Shafranov equilibrium. Therefore, using the same finite element for the computation of initial equilibrium and the evolution of perturbed system, the numerical scheme is well balanced when the projection of the momentum equation use a component parallel to the magnetic field. Indeed, at the discrete level the projection is exactly orthogonal to equilibrium sub-space. Using the potential vector as variable introduces third order derivatives in the system and classical C0 finite elements cannot be directly applied. This is why our finite element strategy uses shape/test functions whose derivatives have global continuity in space. Finite element method is designed for poloidal plane discretization using quadrangles or triangles. Validations have been performed for internal kink and tearing modes instabilities in tokamak with a circular plasma. For this configuration, all magnetic surfaces are closed and simple boundary conditions are used. Future work will address X-point configurations with Bohm boundary conditions.