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.
Highlights
The objective of this work is to present MHD pipe flow of circular cross-section under the influence of a transverse magnetic field numerically by using FEM-BEM coupling approach when the outside medium is electrically conducting
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 streamline upwind Petrov-Galerkin (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
Summary
The objective of this work is to present MHD pipe flow of circular cross-section under the influence of a transverse magnetic field numerically by using FEM-BEM coupling approach when the outside medium is electrically conducting. There are many numerical methods applied to the solution of the MHD pipe flow (see [3,4,5,6,7,8,9] and references there in). The boundary element method is a technique which offers a great advantage to analyze stationary problems especially with infinite domains [10]. BEM has the advantage of discretizing only the pipe wall and gives the solution both in the exterior and interior regions at any point. Due to the regularity conditions, it is possible to limit the discretization to a finite boundary
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