Numerical platform for the interface analysis of magnetic fluids by use of the Boundary Element Method

For the stability analysis or dynamic analysis of the interface phenomena of magnetic fluids as the Rosensweig instability, this paper presents mainly a magnetic analysis with reduced loads, since magnetic fields must be recalculated every time step the interface changes. This method adopts the indirect boundary element method (IBEM), since the behavior of the surface can be explained mainly by the magnetic stress difference obtained from the interface magnetic field. Starting with Green's theorem applied for harmonic fields, the magnetic potential and the normal magnetic induction are obtained separately through the density of singular sources on boundaries. The problems of sharp-pointed peaks on the interface, or edges and corners where boundaries cross are avoided easily. The magnetic field, the interface stresses and the fluid velocity are calculated on the largely-deformed interface in a two-layered system of fluid and vacuum domain under a homogeneous vertical magnetic field. In consideration of the nonlinear equation of motion of the pattern amplitude (Gollwitzer et al., 2010), the sum of interface stresses and the normal fluid velocity are shown in the phase space of the height of the solitarywave interface profile and the intensity of the applied magnetic induction. This IBEM is compared with another method called Magnetic Analysis for General Use (MAGU, Mizuta, 2011) on the formulation basis, and their extension to the nonlinear magnetization is discussed.