First-Order System Least Squares for Incompressible Resistive Magnetohydrodynamics

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 with Maxwell’s equations. This paper shows that the first-order system least squares finite element method (FOSLS) is a viable discretization for these large MHD systems. To solve this system, a nestediteration-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 is 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 f...

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: J. H. Adler, Thomas A. Manteuffel, Stephen F. McCormick, John Ruge
• Keywords: Grant Numbers, Incompressible Resistive Mhd, SIAMSC 2010, Test Problems