Towards an Implicit Highly Scalable Stabilized FE Formulation for Compressible MHD with Application to MCF in Tokamak Geometries

A novel stabilized finite element (FE) discretization of single fluid low Mach number compressible magnetohydrody-namics (MHD) equations is presented. The resulting scheme is used to model macroscopic plasma instabilities in complex 3D Tokamak geometries. A Variational Multiscale Stabilization (VMS) formulation is developed to handle different numerical challenges for the system of equations and the physical regimes of the problems of interest
^1,2
. The discrete systems of equations resulting from a Newton linearization is solved by a preconditioned Krylov method that employs approximate block factorization and Schur complements
³
. Each sub-block solve is approximated as an algebraic multi-grid V-cycle. The numerical tests for ITER relevant problems indicate promising results for different scenarios and benchmarks. Brief results on strong and weak scalability tests are presented that show very good algorithmic performance for large scale problems in different physics regimes.