Abstract
The magnetohydrodynamics (MHD) equation is one of the practical models that it has different applications in physics and engineering. It describes the magnetic properties and behavior of electrically conducting fluids. This paper investigates the MHD equation numerically. First, the time derivative is approximated by utilizing the Crank–Nicholson scheme. The convergence order and unconditional stability of the proposed time-discrete scheme are analyzed by the energy method. Then, the direct meshless local Petrov–Glerkin (DMLPG) method is applied for the spatial derivative to get the full-discrete scheme. The new numerical procedure is used to simulate this equation in a pipe with regular and irregular cross-sectional area. Numerical results show the efficiency of this method is well.
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