Curl-Flow

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