A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

Abstract

This work develops a new monolithic finite-element-based strategy for Magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity-pressure formulation. The entire formula- tion is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.