A Level-Set Method for Magnetic Substance Simulation

Abstract

We present a versatile numerical approach to simulating various magnetic phenomena using a level-set method. At the heart of our method lies a novel two-way coupling mechanism between a magnetic field and a magnetizable mechanical system, which is based on the interfacial Helmholtz force drawn from the Minkowski form of the Maxwell stress tensor. We show that a magnetic-mechanical coupling system can be solved as an interfacial problem, both theoretically and computationally. In particular, we employ a Poisson equation with a jump condition across the interface to model the mechanical-to-magnetic interaction and a Helmholtz force on the free surface to model the magnetic-to-mechanical effects. Our computational framework can be easily integrated into a standard Euler fluid solver, enabling both simulation and visualization of a complex magnetic field and its interaction with immersed magnetizable objects in a large domain. We demonstrate the efficacy of our method through an array of magnetic substance simulations that exhibit rich geometric and dynamic characteristics, encompassing ferrofluid, rigid magnetic body, deformable magnetic body, and multi-phase couplings.

Publication
ACM Transactions on Graphics. 39, 4, Article 29, 15 pages. In Proceedings of the 47th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH 2020)
Xingyu Ni
Xingyu Ni
PhD Student at Center on Frontiers of Computing Studies

My research interests include computational physics, computer graphics, physical simulation and physically based rendering.