The Affine Particle-In-Cell Method

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. Hybrid Lagrangian/Eulerian simulation is commonplace in com-puter graphics for fluids and other materials undergoing large de-formation. 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. Particle-in-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics cal-culations. 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, with-out 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, de-scription 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