A monolithic approach for the solution of the incompressible magnetohydrodynamics equations in two- And three-dimensions

A numerical algorithm has been developed to solve the incompressible magnetohydrodynamics (MHD) equations in a fully coupled form in two- and three-dimensions. The numerical approach is based on the side centered unstructured nite volume approximation where the velocity and magnetic led vector components are defined at the edge/face midpoints, meanwhile the pressure term is defined at the element centroids. In order to enforce a divergence free magnetic eld, a magnetic pressure is introduced to the induction equation. The resulting large-scale algebraic linear equations are solved using a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains. The parallel implementation of the present fully coupled unstructured MHD solver is based on the PETSc library for improving the e ciency of the parallel algorithm. The numerical algorithm is validated for 2D and 3D lid-driven cavity ows with insulating walls.