The affine particle-in-cell method

Abstract

Figure 1: APIC/PIC blends yield more energetic and more stable behavior than FLIP/PIC blends in a wine pour example. APIC/PIC blends are achieved analogously to FLIP/PIC in that it is a scaling of the particle affine matrices. c Disney. AbstractHybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is used for computing mechanical forces and collision responses. Particlein-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics calculations. While these approaches have proven very powerful, they do suffer from some well known limitations. The original PIC is stable, but highly dissipative, while FLIP, designed to remove this dissipation, is more noisy and at times, unstable. We present a novel technique designed to retain the stability of the original PIC, without suffering from the noise and instability of FLIP. Our primary observation is that the dissipation in the original PIC results from a loss of information when transferring between grid and particle representations. We prevent this loss of information by augmenting each particle with a locally affine, rather than locally constant, description of the velocity. We show that this not only stably removes the dissipation of PIC, but that it also allows for exact conservation of angular momentum across the transfers between particles and grid.

MPM Based Simulation for Various Solid Deformation

“…The APIC method [7] can also be implemented to better perserve the information between the interpolation process, which remains to be tested.…”

“…Stomakin et al [12] used MPM for simulating snow, and introduced a novel MPM method for heat transport, melting and solidifying materials [13]. Jiang et al [7] tuned the model in [12] to simulate granular materials. Later Klár et al [8] introduced the Drucker-Prager plastic flow model into MPM to simulate sand dynamics, and Daviet et al [5] presented a semi-implicit scheme for granular materials.…”

“…It is worth mentioning that this approach can handle only small rotations, and approaches like those in [2] or [7] are required to handle larger rotations.…”

Animation of crack propagation by means of an extended multi-body solver for the material point method

“…Yue et al (2015) complemented MPM with a particle re-sampling scheme to handle potential non-uniform particle distributions due to high shearing strain. Jiang et al (2015) proposed to track a locally affine transformation on each particle that would enable conservation of angular momentum; an improvement over the normally used PIC/FLIP [Zhu and Bridson (2005)] update scheme.…”

A multi-scale model for simulating liquid-hair interactions

“…We begin with two standard models for hair and liquid: a particle-in-cell Navier-Stokes liquid simulator [Jiang et al 2015] and a Kirchhoff rod-based hair simulator [Bergou et al 2010]. The observations above motivate our addition of a second fluid model to represent and track liquid directly on the hair itself.…”