The DRBEM solution of incompressible MHD flow equations

Date

2011-12-10

Author

Bozkaya, Nuray
Tezer, Münevver

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This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier-Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function-vorticity-magnetic induction-current density formulation of the full MHD equations in 2D. The stream function and magnetic induction equations which are poisson-type, are solved by using DRBEM with the fundamental solution of Laplace equation. In the DRBEM solution of the time-dependent vorticity and current density equations all the terms apart from the Laplace term are treated as nonhomogeneities. The time derivatives are approximated by an implicit backward difference whereas the convective terms are approximated by radial basis functions. The applications are given for the MHD flow, in a square cavity and in a backward-facing step. The numerical results for the square cavity problem in the presence of a magnetic field are visualized for several values of Reynolds, Hartmann and magnetic Reynolds numbers. The effect of each parameter is analyzed with the graphs presented in terms of stream function, vorticity, current density and magnetic induction contours. Then, we provide the solution of the step flow problem in terms of velocity field, vorticity, current density and magnetic field for increasing values of Hartmann number. Copyright (C) 2010 John Wiley & Sons, Ltd.

Subject Keywords

Mechanical Engineering, Mechanics of Materials, Applied Mathematics, Computational Mechanics, Computer Science Applications

URI

https://hdl.handle.net/11511/40060

Journal

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

DOI

https://doi.org/10.1002/fld.2413

Collections

Department of Mathematics, Article

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Citation Formats

N. Bozkaya and M. Tezer, “The DRBEM solution of incompressible MHD flow equations,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, pp. 1264–1282, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40060.