Liquid-gas free-surface flows in the presence of gravity, surface tension and magnetic field have been numerically studied by using a finite difference method with the HSMAC algorithm. In the numerical simulations, both the two phases (liquid and gas) are assumed to be an incompressible, immiscible, Newtonian fluid and both viscous dissipation and Joule heat are neglected. Therefore, thermal convection due to buoyancy and thermo-capillary effects are not taken into account. The parameters of the present simulations are the Hartmann number (Ha), the Magnetic number (M), the Galilei number (G) and the dimensionless surface tension (Γ) as well as the density, viscosity, susceptibility and conductivity ratios. The numerical results reveal significant difference in the freesurface flows depending on the applied magnetic field not only for the electric conducting fluids (such as mercury and gallium) but also for ordinary non-conducting fluids (such as water and air).
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