Buoyancy-driven Phase Separation in the Material Point Method

The Material Point Method (MPM) provides a unified framework for simulating multi-material systems but struggles to allow for the separation of objects. Traditionally, multi-material simulations use a single background grid, which allows for automatic interaction between materials. Since particles of different types receive their velocities by interpolating from a common background grid, they are unable to efficiently separate. This is especially problematic when simulating immiscible fluids such as oil and water; once oil particles and water particles become mixed, they are unable to separate. A common solution is to solve different objects or materials on separate background grids, which allows particles of different materials to move with different velocities and separate. Using separate background grids loses the natural interaction between materials, since materials no longer interact through the background grid. In the case of immiscible fluids, phase separation is driven by thermodynamics and buoyancy. We present a novel method that enables natural buoyancy-driven phase separation in weakly compressible MPM. Our key observation is that compression and pressure do not depend on the type of particle. A local neighborhood of particles is compressed because particles are close together, and they exert pressure because they bump into the particles that are nearby. Correspondingly, we update the deformation gradient from a unified velocity field and use it to compute a unified pressure force. Combined with the use of separate background grids for velocity, this leads to a treatment of immiscible multiphase fluids that naturally separates due to buoyancy forces, even from a fully mixed configuration. We also propose a mixing potential that is capable of driving phase separation caused by thermodynamics even in the absence of gravity. Finally, we propose a novel algorithm for obtaining consistent per-phase level sets for rendering multiphase particle-based fluids.