Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps

Abstract

Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.

An Efficient Solver for Two‐way Coupling Rigid Bodies with Incompressible Flow

“…Thus, one could design a generalized Multigrid solver for two‐way coupling elastic bodies with incompressible fluids. Finally, it would be interesting to extend our method to thin shells using cut‐cell formulations [AB016].…”

Kinetic-Based Multiphase Flow Simulation

“…While its original formulation exhibits strong numerical diffusion, the Fluid-Implicit-Particle (FLIP) method was later used to mitigate this issue [3], [50]. Ando et al [51] further combined FLIP with adaptive particle sampling, while Cornels et al [52] combined FLIP with SPH; for flows with thin obstacles and narrow gaps, Azevedo et al [53] proposed a modified FLIP method. Additionally, Fu et al [54] addressed the issue of momentum conservation through a polynomial version PIC, based on an earlier affine version [55].…”

An extended cut-cell method for sub-grid liquids tracking with surface tension

“…Stronger two-way coupling between liquids and deformables [Zarifi and Batty 2017] and viscous liquids and solids [Takahashi and Lin 2019] extended previous fractional boundaries approaches. Cut-cells [Azevedo et al 2016;Edwards and Bridson 2014] detach distinct regions of the flow separated by boundaries in a topologically robust way, capturing arbitrarily thin boundaries and narrow gaps. Edwards et al [2014] coupled cut-cells with a p-adaptive Discontinuous Galerkin method for detailed water capturing.…”

“…Thus, we propose an Eulerian fluid solver which captures subgrid features such as thin liquid splashes, narrow air spaces and droplets on regular grids (Figure 2), while still largely conserving the volumes of the embedded liquids. Since our approach is an extension of the cut-cells method [Azevedo et al 2016], it can also naturally handle liquids interacting with complex obstacles (Figures 3 and 6). Our method is enabled by a novel Laplacian solver that handles non grid-aligned Dirichlet boundary conditions.…”