Curl-Flow: Boundary-Respecting Pointwise Incompressible Velocity Interpolation for Grid-Based Fluids

TL;DR

Curl-Flow introduces a boundary-respecting, divergence-free velocity interpolation method for grid-based fluids, improving incompressibility and obstacle interaction accuracy with faster vector potential reconstruction.

Contribution

The paper presents a novel, fast parallel sweeping method for vector potential reconstruction that ensures exact incompressibility and better obstacle handling in fluid simulations.

Findings

Faster vector potential reconstruction compared to prior methods.

Improved particle trajectories respecting obstacles and incompressibility.

Enhanced particle distribution quality over time.

Abstract

We propose to augment standard grid-based fluid solvers with pointwise divergence-free velocity interpolation, thereby ensuring exact incompressibility down to the sub-cell level. Our method takes as input a discretely divergence-free velocity field generated by a staggered grid pressure projection, and first recovers a corresponding discrete vector potential. Instead of solving a costly vector Poisson problem for the potential, we develop a fast parallel sweeping strategy to find a candidate potential and apply a gauge transformation to enforce the Coulomb gauge condition and thereby make it numerically smooth. Interpolating this discrete potential generates a pointwise vector potential whose analytical curl is a pointwise incompressible velocity field. Our method further supports irregular solid geometry through the use of level set-based cut-cells and a novel Curl-Noise-inspired potential ramping procedure that simultaneously offers strictly non-penetrating velocities and incompressibility. Experimental comparisons demonstrate that the vector potential reconstruction procedure at the heart of our approach is consistently faster than prior such reconstruction schemes, especially those that solve vector Poisson problems. Moreover, in exchange for its modest extra cost, our overall Curl-Flow framework produces significantly improved particle trajectories that closely respect irregular obstacles, do not suffer from spurious sources or sinks, and yield superior particle distributions over time.