First-Order System Least Squares for Incompressible Resistive Magnetohydrodynamics. - Adler, James H.; Manteuffel, Thomas Albert, 1948-; McCormick, S. F. (Stephen Fahrney), 1944-; Ruge, John.; Sanders, G.D. (Tufts University. Tisch Library., 2017)
Magnetohydrodynamics (MHD) is a fluid theory that describes plasma physics by treating the plasma as a fluid of charged particles. Hence, the equations that describe the plasma form a nonlinear system that couples Navier-Stokes equations with Maxwell's equations. This paper shows that the first-order system least squares (FOSLS) finite element method is a viable discretization for these large MHD systems. To solve this system, a nested-iteration-Newton-FOSLS-AMG approach is taken. Most of the work is done on the coarse grid, including most of the linearizations. We show that at most one Newton step and a few V-cycles are all that are needed on the finest grid. Here, we describe how the FOSLS method can be applied to incompressible resistive MHD and how it can be used to solve these MHD problems efficiently. A 3D steady state and a reduced 2D time-dependent test problem are studied. The latter equations can simulate a "large aspect-ratio" tokamak. The goal is to resolve as much physics from the test problems with the least amount of computational work. We show that this is achieved in a few dozen work units or fine grid residual evaluations.