Meshless local boundary integral equation (LBIE) method for the unsteady magnetohydrodynamic (MHD) flow in rectangular and circular pipes |
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Authors: | Mehdi Dehghan Davoud Mirzaei |
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Affiliation: | Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., 15914 Tehran, Iran |
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Abstract: | The meshless local boundary integral equation (LBIE) 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 and circular sections with non-conducting walls. Computations have been carried out for different Hartmann numbers and at various time levels. The method is based on the local boundary integral equation with 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 to show the behaviour of velocity and induced magnetic field. |
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Keywords: | Unsteady MHD flow Meshless local boundary integral equation (LBIE) Companion solution Moving least squares (MLS) approximation |
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