An Efficiency-Based Adaptive Refinement Scheme Applied to Incompressible, Resistive Magnetohydrodynamics

Abstract

AbstractThis paper describes the use of an efficiency-based adaptive mesh refinement scheme, known as ACE, on a 2D reduced model of the incompressible, resistive magnetohydrodynamic (MHD) equations. A first-order system least squares (FOSLS) finite element formulation and algebraic multigrid (AMG) are used in the context of nested iteration. The FOSLS a posteriori error estimates allow the nested iteration and ACE algorithms to yield the best accuracy-per-computational-cost. The ACE scheme chooses which elements to add when interpolating to finer grids so that the best error reduction with the least amount of cost is obtained, when solving on the refined grid. We show that these methods, applied to the simulation of a tokamak fusion reactor instability, yield approximations to solutions within discretization accuracy using less than the equivalent amount of work needed to perform 10 residual calculations on the finest uniform grid.KeywordsMagnetohydrodynamicsadaptive mesh refinementalgebraic multigridnested iteration