  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.
