Computational modeling of magnetoconvection: Effects of discretization method, grid refinement and grid stretching

The problem of natural convection in a laterally heated three-dimensional cubic cavity under the action of an externally imposed magnetic field is revisited. Flows at the Rayleigh number Ra=10⁶ and the Hartmann number Ha=100, and three different orientations of the magnetic field are considered. The problem is solved using two independent numerical methods based on the second order finite-volume discretization schemes on structured Cartesian grids. Convergence toward grid-independent results is examined versus the grid refinement and near-wall grid stretching. Converged benchmark-quality results are obtained. It is shown that for convection flows with a strong magnetic field a steep, sometimes extremely steep, stretching near some of the boundaries is needed. Three-dimensional patterns and integral properties of the converged flow fields are reported and discussed. It is shown that the strongest magnetic suppression is yielded by the field directed along the imposed temperature gradient. The horizontal magnetic field perpendicular to the imposed temperature gradient stabilizes the main convection roll and leads to a flow with higher kinetic energy and heat transfer rate than in the non-magnetic case. Applicability of the quasi-two-dimensional model to natural convection flows in a box is discussed.