R-T instability model of magnetic fluid and its numerical simulations

The Rayleigh-Taylor(R-T) instability of ferrofluid has been the subject of recent research, because of its implications on the stability of stellar. By neglecting the viscosity and rotation of magnetic fluid, and assuming that the magnetic particles are irrotational and temperature insensitive, we obtain a simplified R-T instability model of magnetic fluid. For the interface tracing, we use five-order weighted essentially non-oscillatory(WENO) scheme to spatial direction and three-order TVD R-K method to time direction on the uniform mesh, respectively. If the direction of the external magnetic field is the same as that of gravity, the velocities of the interface will be increased. But if the direction of the external magnetic field is in opposition to the direction of gravity, the velocities of the interface will be decreased. When the direction of the external magnetic field is perpendicular to the direction of gravity, the symmetry of the interface will be destroyed. Because of the action which is produced by perpendicular external magnetic field, there are other bubbles at the boudaries which parallel the direction of gravity. When we increase the magnetic susceptibility of the magnetic fluids, the effects of external magnetic fields will be more distinct for the interface tracing.