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Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time-integration scheme. (English) Zbl 1089.76040
Summary: 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 magnetohydrodynamic (MHD) flow problem in a rectangular duct with insulating walls. The coupled MHD equations for velocity and induced magnetic field are transformed first into decoupled time-dependent convection-diffusion-type equations. These equations are solved by using DRBEM which treats the time and space derivatives as nonhomogeneity, and then by using DQM for the resulting system of initial value problems. The resulting linear system of equations is overdetermined due to the imposition of both boundary and initial conditions. Employing the least square method to this system, the solution is obtained directly at any time level without the need of step-by-step computation with respect to time. Computations have been carried out for moderate values of Hartmann number $(M\leqslant 50)$ at transient and steady-state levels. As $M$ increases, boundary layers are formed for both the velocity and the induced magnetic field, and the velocity becomes uniform at the centre of the duct. Also, the higher is the value of $M$ the smaller is the value of time for reaching steady-state solution.

76M15Boundary element methods (fluid mechanics)
76M25Other numerical methods (fluid mechanics)
76W05Magnetohydrodynamics and electrohydrodynamics
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