A finite element method for magnetohydrodynamics Original Research Article

This paper presents a finite element method for the solution of 3D incompressible magnetohydrodynamic (MHD) flows. Two important issues are thoroughly addressed. First, appropriate formulations for the magnetic governing equations and the corresponding weak variational forms are discussed. The selected (B,q) formulation is conservative in the sense that the local divergence-free condition of the magnetic field is accounted for in the variational sense. A Galerkin-least-squares variational formulation is used allowing equal-order approximations for all unknowns. In the second issue, a solution algorithm is developed for the solution of the coupled problem which is valid for both high and low magnetic Reynolds numbers. Several numerical benchmark tests are carried out to assess the stability and accuracy of the finite element method and to test the behavior of the solution algorithm.