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A stabilized element-free Galerkin (EFG) method is proposed in this paper for numerical analysis of the generalized steady MHD duct flow problems at arbitrary and high Hartmann numbers up to 1016\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs...
Citations
... In [15], a stabilized FEM with shock-capturing is tested for steady and unsteady MHD equations to handle the convection dominance as a result of the high Ha values. Li and Li [16] developed a stabilized element-free Galerkin method to solve time-independent MHD duct problems for Ha ∈ [1, 10 6 ]. Marusic-Paloka [17] obtained the asymptotic solutions of velocity and induced MF to analyze the impact of slip condition and perturbation of the boundary. ...
In this study, a machine learning approach to unsteady magnetohydrodynamic (MHD) flow is investigated in a square duct under the effect of an inclined magnetic field for the first time. Induced magnetic field is also taken into consideration. The duct walls are impermeable and the velocity has no-slip boundary conditions. The global radial basis function method and the backward Euler method are implemented for the space and the time discretization, respectively, in velocity and induced magnetic field equations. The datasets from the numerical results of MHD equations are stored for the range of problem variables which are Reynolds, magnetic Reynolds and Hartmann numbers, and the inclination angle of the applied magnetic field. Neural Network (NN) algorithm is utilized for modeling velocity and induced magnetic field inside the duct at the steady state by using values both in range and out of the range values. Average values of velocity and induced magnetic field are also estimated at any time level. The capability of NN to get good metric results reveals that the machine learning approach may provide independence from recurrent numerical calculations.
