DRBEM Solution of Incompressible MHD Flow with Magnetic Potential

Pekmen, B.
Tezer, Münevver
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.


DRBEM applications in fluid dynamics problems and DQM solutions of hyperbolic equations
Pekmen, Bengisen; Tezer Sezgin, Münevver; Department of Scientific Computing (2014)
In this thesis, problems of fluid dynamics defined by the two-dimensional convection-diffusion type partial differential equations (PDEs) are solved using the dual reciprocity boundary element method (DRBEM). The terms other than the Laplacian are treated as inhomogeneous terms in the DRBEM application. Once the both sides are multiplied by the fundamental solution of Laplace equation, and then integrated over the domain, all the domain integrals are transformed to boundary integrals using the Green's ident...
DRBEM Solution of MHD Flow and Electric Potential in a Rectangular Pipe with a Moving Lid
Tezer, Münevver; Bozkaya, Canan (2015-09-18)
We present the dual reciprocity boundary element method (DRBEM) solution of the system of equations which model magnetohydrodynamic (MHD) flow in a pipe with moving lid at low magnetic Reynolds number. The external magnetic field acts in the pipe-axis direction generating the electric potential. The solution is obtained in terms of stream function, vorticity and electric potential in the cross-section of the pipe, and the pipe axis velocity is also computed under a constant pressure gradient. It is found th...
DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations
Meral, Guelnihal; Tezer, Münevver (Elsevier BV, 2010-06-01)
The nonlinear wave equation is solved numerically in an exterior region For the discretization of the space derivatives dual reciprocity boundary element method (DRBEM) is applied using the fundamental solution of Laplace equation. The time derivative and the nonlinearity are treated as the nonhomogenity. The boundary integrals coming from the far boundary are eliminated using rational and exponential interpolation functions which have decay properties far away from the region of Interest. The resulting sys...
DRBEM solution of free convection in porous enclosures under the effect of a magnetic field
Pekmen, B.; Tezer, Münevver (2013-01-01)
The dual reciprocity boundary element method (DRBEM) is applied for solving steady free convection in special shape enclosures filled with a fluid saturated porous medium under the effect of a magnetic field. The left and right walls are maintained at constant or different temperatures while the top and bottom walls are kept adiabatic. The effect of the external magnetic field on the flow and temperature behavior is visualized with different Rayleigh numbers Ra, Hartmann numbers Ha and inclination angle phi...
DRBEM solutions of cauchy problem for the magnetohydrodynamic duct flow
Aydın, Cemre; Tezer-Sezgin, Münevver,; Department of Mathematics (2020)
In this thesis, the direct and inverse problems of the MHD flow in rectangular ducts are solved in terms of the velocity of the fluid and the induced magnetic field by using the Dual Reciprocity Boundary Element Method (DRBEM). The two-dimensional, steady flow of a viscous, incompressible, and electrically conducting fluid is considered under the effect of an externally applied mangetic field. The duct wall conditions for the MHD flow ranges from the no-slip to slip and insulated to perfectly conducting. In...
Citation Formats
B. Pekmen and M. Tezer, “DRBEM Solution of Incompressible MHD Flow with Magnetic Potential,” CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, pp. 275–292, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53457.