Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem

Seda Demir and Harun Selvitopi ()
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Seda Demir: Department of Mathematics, Faculty of Science, Erzurum Technical University, 25100 Erzurum, Türkiye
Harun Selvitopi: Department of Mathematics, Faculty of Science, Erzurum Technical University, 25100 Erzurum, Türkiye

Mathematics, 2024, vol. 12, issue 22, 1-11

Abstract: Magnetohydrodynamic (MHD) flow plays a crucial role in various applications, ranging from nuclear fusion devices to MHD pumps. The mathematical modeling of such flows involves convection–diffusion-type equations, with fluid velocity governed by the Navier–Stokes equations and the magnetic field determined by Maxwell’s equations through Ohm’s law. Due to the complexity of these models, most studies on steady and unsteady MHD equations rely on numerical methods, as theoretical solutions are limited to specific cases. In this research, we propose a damped-wave-type mathematical model to describe fluid flow within a channel, taking into account both the velocity and magnetic field components. The model is solved numerically using the finite difference method for time discretization and the finite element method for spatial discretization. Numerical results are displayed graphically for different values of Hartmann numbers, and a detailed analysis and discussion of the solutions are provided.

Keywords: magnetohydrodynamic fluid flow problem; finite element method; finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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