Mathematical modeling of incompressible MHD flows with free surface

Abstract

Mathematical model for incompressible magnetohydrodynamics (MHD) flows with complex free surfaces has been developed, the transient 3D Navier-Stokes equations with Lorentz force induced by static magnetic field are solved. In this model, the simplified marker and cell (SMAC) method is used for solving the Navier-Stokes equations, the dynamic conditions at free surface are implemented through the continuum surface force (CSF) model with the volume of fluid (VOF) method, the compressive interface capturing scheme for arbitrary meshes (CICSAM) scheme is used for the VOF convection, and anti-diffusion procedure is conducted to suppress the numerical diffusion caused by the VOF convection. Effect of the anti-diffusion operation is investigated, and coalescence of two gas bubbles and impact of a drop on shallow liquid film are examined in order to verify the validity of the present mathematical model. As MHD flow examples, pouring of liquid metal into a rectangle insulated container and coalescence of two gas bubbles in the static magnetic field are simulated. © 2007 ISIJ.