Month: June 2020

Xingyu Ni, Bo Zhu, Bin Wang, Baoquan Chen

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.

A Level-Set Method for Magnetic Substance Simulation

Hui Wang, Yongxu Jin, Anqi Luo, Xubo Yang, Bo Zhu

We propose a new Eulerian-Lagrangian approach to simulate the various surface tension phenomena characterized by volume, thin sheets, thin filaments, and points using Moving-Least-Squares (MLS) particles. At the center of our approach is a meshless Lagrangian description of the different types of codimensional geometries and their transitions using an MLS approximation. In particular, we differentiate the codimension-1 and codimension-2 geometries on Lagrangian MLS particles to precisely describe the evolution of thin sheets and filaments, and we discretize the codimension-0 operators on a background Cartesian grid for efficient volumetric processing. Physical forces including surface tension and pressure across different codimensions are coupled in a monolithic manner by solving one single linear system to evolve the surface-tension driven Navier-Stokes system in a complex non-manifold space. The codimensional transitions are handled explicitly by tracking a codimension number stored on each particle, which replaces the tedious meshing operators in a conventional mesh-based approach. Using the proposed framework, we simulate a broad array of visually appealing surface tension phenomena, including the fluid chain, bell, polygon, catenoid, and dripping, to demonstrate the efficacy of our approach in capturing the complex fluid characteristics with mixed codimensions, in a robust, versatile, and connectivity-free manner.

Codimensional Surface Tension Flow using Moving-Least-Squares Particles