Surface-only ferrofluids

Abstract

Numerical integration procedure updating the state (i.e. vertex positions and velocities) of the magnetic fluid. Input: Current fluid state. Output: Updated fluid state. 1 Advection; Section 4.1. 2 Enforce harmonic velocity by Helmholtz decomposition; Section 4.2. 3 Calculate surface tension and gravity potential. Section 4.3. 4 Calculate magnetic pressure using Algorithm 2. 5 Solve the pressure using a BEM; Section 4.5. 6 Apply the negative gradient of the pressure to the velocity. ALGORITHM 2: Evaluation procedure of the magnetic pressure. Input: Vertex positions. Output: Magnetic pressure at vertices. 1 Update the external magnetic field. 2 Evaluate the external magnetic scalar potential; Section 4.4.1. 3 Calculate magnetic double layer charges at vertices; Section 4.4.2. 4 Evaluate magnetic pressure discontinuities at vertices; Section 4.4.4.

Ships, Splashes, and Waves on a Vast Ocean

“…More complex solid behaviors like fracture can also be captured and accelerated through the BEM ]. The BEM is adopted for simulating various fluid phenomena including large scale deep ocean waves [Keeler and Bridson 2015], fluid chains, water droplets [Da et al 2016a] and even magnetic fluids [Huang and Michels 2020]. Besides, BEM has also been adopted in sound rendering [Zheng and James 2010] and geometry processing [Solomon et al 2017].…”

“…and solving a Laplace equation with mixed boundary condition. We refer the reader to the work of Da et al [2016a] and the work of Huang and Michels [2020] for details. We prefer the H.D.…”

“…The interpolation point 𝑥 can still be close to the quadrature point and introduce error. The easy solution is to use nearest neighbor interpolation, or one can apply the more expensive analytic integration of the fundamental solution 1/|𝑥 − 𝑦| over triangles, as adopted by Huang and Michels [2020]. The brute force integration for each position on the FLIP boundary is expensive.…”

“…The BEM part is based on the open source code of Da et al [2016b] with CUDA acceleration provided by Huang and Michels [2020] on our request. The FLIP code is based on the open source implementation of Batty et al [2007] and Ng et al [2009] provided by Batty [2018].…”

“…The search step size is half of the FLIP voxel size. The projection step of the BEM is a Galerkin boundary element method as described and implemented by Huang and Michels [2020].…”