APPM Department Colloquium - Luis Chacon

Luis Chacon, Los Alamos National Laboratory

On fully implicit methods for extended magnetohydrodynamics

Magnetohydrodynamics (MHD) describes the behavior of charged hot gases (plasmas) in the presence of electromagnetic fields, and is a crucial tool for the understanding of solar, space, and laboratory (e.g. thermonuclear fusion) plasmas. Mathematically, MHD is a hyperbolic PDE system which supports various fast waves. In its basic form (single fluid MHD), these waves are linear (k). However, in extended (or two-fluid) MHD models (XMHD), these waves become dispersive (k2). THe numerical stiffness associated with such waves present severe challenges for the efficient and accurate numerical integration of MHD phenomena over long frequencies. In this talk, we describe our discretization/solver strategy to address such challenges. Spatially, we employ Newton-Krylov-based fully implicit methods for robustness, efficiency, and accuracy. A crucial aspect of our approach is a novel preconditioning strategy, which we term “physics-based”. It os based on a Schur complement treatment of the semi-discrete MHD equations, which in turn renders the linearized MHD system well conditioned for the use of classical multilevel techniques, thereby resulting in an optimal, scalable MHD solver.