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N. B. Salah, A. Soulaimani, W. G. Habash and M. Fortin, “A Conservative Stabilized Finite Element Method for the Magneto-Hydrodynamic Equations,” International Journal for Numerical Methods in Fluids, Vol. 29, No. 5, 1999, pp. 535-554. doi:10.1002/(SICI)1097-0363(19990315)29:5<535::AID-FLD799>3.0.CO;2-D

has been cited by the following article:

• TITLE: FEM-BEM Coupling for the MHD Pipe Flow in an Exterior Region

  AUTHORS: S. Han Aydin

  KEYWORDS: FEM-BEM Coupling; SUPG; MHD Pipe Flow

  JOURNAL NAME: Open Journal of Fluid Dynamics, Vol.3 No.3, September 18, 2013

  ABSTRACT: In this study, the magnetohydrodynamic (MHD) flow through a circular pipe under the influence of a transverse mag- netic field when the outside medium is also electrically conducting is solved numerically by using FEM-BEM coupling approach. The coupled partial differential equations defined for the interior medium are transformed into homogenous modified Helmholtz equations. For the exterior medium on an infinite region, the Laplace equation is considered for the exterior magnetic field. Unknowns in the equations are also related with the corresponding Dirichlet and Neumann type coupled boundary conditions. Unknown values of the magnetic field on the boundary and for the exterior region are obtained by using BEM, and the unknown velocity and magnetic field inside the pipe are obtained by using SUPG type stabilized FEM. Computations are carried for very high values of magnetic Reynolds numbers Rm1, Reynolds number Re and magnetic pressure Rh of the fluid. The results show that using stabilized method enables us to get stable and accurate numerical approximations consistent with the physical configuration of the problem over rough mesh which also results a cheap computational cost.