Three-dimensional numerical simulation for magnetohydrodynamic duct flows in a staggered grid system

Liquid metal flow in a rectangular duct subjected to a strong external magnetic field is numerically simulated by three-dimensional SIMPLE algorithm on a finite volume structured staggered grid. The current density and the Lorentz force are calculated by solving the electrical potential equation at low magnetic Reynolds numbers and high Hartmann numbers with consistent and conservative scheme. The Crank–Nicolson scheme is used to update the convective and diffusion terms to get a second-order temporal accuracy. The diffusion and convective term is discretised by a second order central difference scheme. The code is verified by simulating Shercliff's case and Hunt's case II with different Hartmann number and Reynolds number. Numerical results have a good agreement with the analytical solution.