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

Authors: N. Alsoy-Akgün; M. Tezer-Sezgin

Addresses: Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey ' Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey

Abstract: 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 10⁶ 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.

Keywords: dual reciprocity BEM; boundary element method; DRBEM; differential quadrature method; DQM; natural convection flow; MHD; cavities; magnetic field; magnetohydrodynamics.

DOI: 10.1504/PCFD.2013.055056

Progress in Computational Fluid Dynamics, An International Journal, 2013 Vol.13 No.5, pp.270 - 284

Published online: 31 Oct 2013 *

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