Curl-Flow: Pointwise Incompressible Velocity Interpolation forGrid-Based Fluids

We propose a novel methodology to enhance grid-based fluid animation with pointwise divergence-free velocity interpolation. Our method takes as input a discretely divergence-free staggered grid velocity field generated by a standard pressure projection, and first recovers a consistent corresponding edge-based discrete vector potential in 3D (or node-based stream function in 2D). We interpolate these values to form a pointwise potential, and apply the continuous curl operator to recover a pointwise flow field that is perfectly incompressible. Our method supports irregular geometry through the use of level set-based cut-cells. To recover a smooth and velocity-consistent discrete vector potential in 3D, we employ a sweeping approach followed by a gauge correction that requires a single scalar Poisson solve, rather than a vector Poisson problem. In both 2D and 3D, we show how modified interpolation strategies can be applied to better account for the presence of irregular cut-cell boundaries. Our results demonstrate that our overall proposed Curl-Flow framework produces significantly better particle trajectories that suffer from far fewer spurious sources or sinks, respect irregular obstacles, and better preserve particle distributions over time.