Towards a scalable fully-implicit VMS formulation for compressible visco-resistive MHD for application to MCF in Tokamak relevant geometries
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A novel stabilized finite element (FE) discretization of single fluid low Mach number compressible magnetohydrodynamics (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 system 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 is approximated as an algebraic multigrid V-cycle. Several numerical tests have been performed to assess the correctness of the formulation for ITER relevant problems. The results 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 for large problems in different regimes. [1] J. Bonilla, J.N. Shadid, X-Z. Tang, P. Ohm, M. Crockatt, R.P. Pawlowski, and S. Conde, A scalable fully-implicit stabilized FE formulation for compressible viscoresistive MHD with application to Tokamak simulations, In preparation. [2] J.N. Shadid, R.P. Pawlowski, E.C. Cyr, R.S. Tuminaro, L. Chacón, and P.D. Weber, Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton-Krylov-AMG, Computer Methods in Applied Mechanics and Engineering 304 (2016) 1–25. [3] P. Ohm, J. Bonilla, E. Phillips, J.N. Shadid, R. S. Tuminaro, J. J. Hu, Operator-Splitting based block preconditioning for Tokamak ITER VDE simulations, In preparation. U.S. DOE supported this work through the Fusion Theory Program of FES, and the Tokamak Disruption Simulation (TDS) SciDAC partnerships between FES and ASCR. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. LANL is managed by Triad National Security, LLC, for DOE’s NNSA. LA-UR-23-21031
