Surface-only ferrofluids

Abstract

We devise a novel surface-only approach for simulating the three dimensional free-surface flow of incompressible, inviscid, and linearly magnetizable ferrofluids. A Lagrangian velocity field is stored on a triangle mesh capturing the fluid's surface. The two key problems associated with the dynamic simulation of the fluid's interesting geometry are the magnetization process transitioning the fluid from a non-magnetic into a magnetic material, and the evaluation of magnetic forces. In this regard, our key observation is that for linearly incompressible ferrofluids, their magnetization and application of magnetic forces only require knowledge about the position of the fluids' boundary. Consequently, our approach employs a boundary element method solving the magnetization problem and evaluating the so-called magnetic pressure required for the force evaluation. The magnetic pressure is added to the Dirichlet boundary condition of a surface-only liquids solver carrying out the dynamical simulation. By only considering the fluid's surface in contrast to its whole volume, we end up with an efficient approach enabling more complex and realistic ferrofluids to be explored in the digital domain without compromising efficiency. Our approach allows for the use of physical parameters leading to accurate simulations as demonstrated in qualitative and quantitative evaluations.