An adaptive Particle-In-Cell method for liquid simulation using RBF-FD - Nakanishi, Rafael Umino (2021)
Adaptive data structures have become of interest for processing large amounts of information, mainly due to their ability to automatically model the data format. We introduced a new approach in the liquid simulation that combines the pressure projection method with the Particle-In-Cell (PIC) method. The solver relies on a generalized version of the Finite Difference (FD) method to approximate the pressure field and its gradients in tree-based grid discretizations, possibly non-graded. In our approach, FD stencils are computed using mesh-free interpolations provided by a variant of Radial Basis Function (RBF), known as RBF-Finite-Difference (RBF-FD). This mesh-free version of the FD produces differentiation weights on scattered nodes with high-order accuracy. Our method adapts a quadtree/octree dynamically in a narrow-band around the liquid interface, providing an adaptive particle sampling for the PIC advection step. Furthermore, RBF affords an accurate scheme for velocity transfer between the grid and particles, keeping the systems stability and avoiding numerical dissipation. We also present a data structure that connects the spatial subdivision of a quadtree/octree with the topology of its corresponding dual-graph. Our data structure makes the setup of stencils straightforward, allowing its updating without the need to rebuild it from scratch at each time-step. We show our solvers effectiveness and accuracy by simulating incompressible inviscid fluids and comparing results with regular PIC-based solvers available in the literature.