DRBEM and DQM solutions of natural convection flow in a cavity under a magnetic field

The dual reciprocity boundary element method (DRBEM) and the differential quadrature method (DQM) are applied to solve the 2D, unsteady natural convection flow in enclosures under an externally applied magnetic field. Vorticity transport and energy equations are transformed to modified Helmholtz equations by utilising forward difference with relaxation parameters for the time derivatives, and approximating also Laplacian terms at two consecutive time levels. Thus, the need of another time integration scheme and very small time increment is eliminated. Inhomogeneities in modified Helmholtz equations are approximated with two types of radial basis functions. Solutions are obtained with both DRBEM and DQM for Ra and Ha values up to 10(6) and 300; respectively, and compared. DRBEM and DQM give almost the same accuracy, but DQM uses considerably small number of grid points resulting with less computational work.