Interface analysis of magnetic fluids by the boundary element method considering multiplicity and singularity

Abstract

The present paper is devoted for numerical analysis of interface phenomena of magnetic fluids in real space and time, when the Boundary Element Method (BEM) is employed. The BEM obtains not only the magnetic potential and the normal magnetic induction for static magnetic fields but also the fluid velocity potential and the normal fluid velocity for incompressible–irrotational fluids, on arbitrary-shaped interfaces. During the discretizing process, one of the problems is the multiplicity, that is, multi-valued physical quantities at the edges and corners of the domains, or sharp-pointed peaks on the interface. Another problem is the singularity in the diagonal discretization terms, which is inherent to the BEM. Discretization elements at the same position are grouped for the multiplicity. The sum rules for discretization coefficients are used to avoid the singularity, which is derived from the uniform vector field conditions as the extension from the conventional one. Based on the formulated equations, a computational code was produced, and applied for simplified and more general conditions. This code generates magnetic fields on the interface between the fluid and the vacuum as intended with the least numerical effects. It also generates the fluid velocity caused by ununiform distribution of the sum of interface stresses. The applicability for the stability analysis on the Rosensweig instability is also discussed.