Development of a convection–diffusion‐reaction magnetohydrodynamic solver on non‐staggered grids

This paper presents a convection–diffusion-reaction (CDR) model for solving magnetic induction equations and incompressible Navier–Stokes equations. For purposes of increasing the prediction accuracy, the general solution to the one-dimensional constant-coefficient CDR equation is employed. For purposes of extending this discrete formulation to two-dimensional analysis, the alternating direction implicit solution algorithm is applied. Numerical tests that are amenable to analytic solutions were performed in order to validate the proposed scheme. Results show good agreement with the analytic solutions and high rate of convergence. Like many magnetohydrodynamic studies, the Hartmann–Poiseuille problem is considered as a benchmark test to validate the code. Copyright © 2004 John Wiley & Sons, Ltd.