Meshless Local Petrov--Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity

Authors:
Mehdi Dehghan;Davoud Mirzaei
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 3
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Abstract

In this article a meshless local Petrov-Galerkin (MLPG) method is given to obtain the numerical solution of the coupled equations in velocity and magnetic field for unsteady magnetohydrodynamic (MHD) flow through a pipe of rectangular section having arbitrary conducting walls. Computations have been carried out for different Hartmann numbers and wall conductivity at various time levels. The method is based on the local weak form and the moving least squares (MLS) approximation. For the MLS, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. A time stepping method is employed to deal with the time derivative. Finally numerical results are presented showing the behaviour of velocity and induced magnetic field across the section.