Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations

In this study, the solution of the steady magnetohydrodynamic (MHD) equations is considered on various 2D and 3D closed domains (triangle, tetrahedron, pyramid and conic) and channel configurations such as swollen channel, collapsed channel, narrowed channel and wrinkled curved channel which are encountered in many real-life applications. As a numerical procedure both stabilized finite element method (FEM) and coupled dual reciprocity boundary element method (DRBEM) formulation are used. The coupled DRBEM is different from the previous literature on decoupled DRBEM, and it enables the use of different boundary condition types that are proposed for the moderate and high Hartmann number values. The other benefit of coupled DRBEM is that it combines all the coefficients of the unknown variables including the normal derivatives into a single coefficient matrix, therefore in one computation stroke one finds the solution to the problem. The wrinkled curved channel flow may be applied to the analysis of blood flow under the influence of an externally applied magnetic field in the stenosed artery. Some numerical calculations were performed for the different problem parameters and boundary conditions. The comparison of the results for some test problems using the proposed numerical schemes are presented in tables and contour plots.