The two-level element free Galerkin method for MHD flow at high Hartmann numbers

In this Letter, a new element free Galerkin method, namely the two-level element free Galerkin method, is presented for solving the governing equations of steady magnetohydrodynamic duct flow. Because this element free Galerkin method makes use of the nodal point configurations which do not require a mesh, therefore it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. Another distinguished feature of the proposed method is the resolving capability of high gradients near the layer regions without local or adaptive refinements. Numerical results indicate that no matter how large the Hartmann number is, this method has the ability to produce the satisfactory results for the velocity and the magnetic field simultaneously. That is to say, the presented method has some excellent properties, such as better stability and accuracy.