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DRBEM Solution of Incompressible MHD Flow with Magnetic Potential

B. Pekmen1,2, M. Tezer-Sezgin2,3

Department of Mathematics, Atılım University, 06836, Ankara, Turkey
Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey
Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

Computer Modeling in Engineering & Sciences 2013, 96(4), 275-292.


The dual reciprocity boundary element method (DRBEM) formulation is presented for solving incompressible magnetohydrodynamic (MHD) flow equations. The combination of Navier-Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetics through Ohm’s law is considered in terms of stream function, vorticity and magnetic potential in 2D. The velocity field and the induced magnetic field can be determined through the relations with stream function and magnetic potential, respectively. The numerical results are visualized for several values of Reynolds (Re), Hartmann (Ha) and magnetic Reynolds number (Rem) in a lid-driven cavity, and in a channel with a square cylinder. The well-known characteristics of the fluid flow and MHD flow are exhibited. These are the shift of the core region of the flow and the development of the main vortex in the vorticity through the center of the cavity as Re increases. An increase in Ha causes Hartmann layers for the flow at the bottom and top walls. Higher values of Rem result in circulation of the magnetic potential at the center of the cavity. An increase in Re causes symmetric vortices behind the cylinder to elongate through the channel, and an increase in Hartmann number suppresses this elongation.


Cite This Article

Pekmen, B., Tezer-Sezgin, M. (2013). DRBEM Solution of Incompressible MHD Flow with Magnetic Potential. CMES-Computer Modeling in Engineering & Sciences, 96(4), 275–292.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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