The DRBEM solution of incompressible MHD flow equations

2011-12-10
Bozkaya, Nuray
Tezer, Münevver
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.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

Suggestions

Solution to transient Navier-Stokes equations by the coupling of differential quadrature time integration scheme with dual reciprocity boundary element method
Bozkaya, Canan; Tezer, Münevver (Wiley, 2009-01-20)
The two-dimensional time-dependent Navier-Stokes equations in terms of the vorticity and the stream function are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in space with the differential quadrature method (DQM) in time. In DRBEM application, the convective and the time derivative terms in the vorticity transport equation are considered as the nonhomogeneity in the equation and are approximated by radial basis functions. The solution to the Poisson equati...
The finite element method for MHD flow at high Hartmann numbers
Nesliturk, AI; Tezer, Münevver (Elsevier BV, 2005-01-01)
A stabilized finite element method using the residual-free bubble functions (RFB) is proposed for solving the governing equations of steady magnetohydrodynamic duct flow. A distinguished feature of the RFB method is the resolving capability of high gradients near the layer rep-ions without refining mesh. We show that the RFB method is stable by proving that the numerical method is coercive even not only at low values but also at moderate and high values of the Hartmann number. Numerical results confirming t...
A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows
Eroglu, Fatma G.; Kaya Merdan, Songül; Rebholz, Leo G. (Elsevier BV, 2017-10-01)
In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The projection-based VMS stabilization is added as a separate post-processing step to the standard POD approximation, and since the stabilization step is completely decoupled, the method can easily be incorporated into existing codes, and stabilization parameters can be tuned independe...
An adaptive fully discontinuous Galerkin level set method for incompressible multiphase flows
KARAKUS, Ali; WARBURTON, Tim; AKSEL, MEHMET HALUK; Sert, Cüneyt (Emerald, 2018-01-01)
Purpose This study aims to focus on the development of a high-order discontinuous Galerkin method for the solution of unsteady, incompressible, multiphase flows with level set interface formulation.
Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme
Bozkaya, Canan; Tezer, Münevver (Wiley, 2006-06-20)
A numerical scheme which is a combination of the dual reciprocity boundary element method (DRBEM) and the differential quadrature method (DQM), is proposed for the solution of unsteady magnetohydro-dynamic (MHD) flow problem in a rectangular duct with insulating walls. The coupled MHD equations in velocity and induced magnetic field are transformed first into the decoupled time-dependent convection-diffusion-type equations. These equations are solved by using DRBEM which treats the time and the space deriva...
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.