Sheu, Tony W. H.; Lin, R. K. Development of a convection-diffusion-reaction magnetohydrodynamic solver on non-staggered grids. (English) Zbl 1060.76619 Int. J. Numer. Methods Fluids 45, No. 11, 1209-1233 (2004). Summary: 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. Cited in 19 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76W05 Magnetohydrodynamics and electrohydrodynamics 76R99 Diffusion and convection 76V05 Reaction effects in flows Keywords:Convection-diffusion-reaction; magnetic induction equations; incompressible; Navier-Stokes; Hartmann-Poiseuille PDFBibTeX XMLCite \textit{T. W. H. Sheu} and \textit{R. K. Lin}, Int. J. Numer. Methods Fluids 45, No. 11, 1209--1233 (2004; Zbl 1060.76619) Full Text: DOI