Divergence projection with electrostatics

Abstract

The pressure component of the Navier-Stokes equation can be solved by projecting out the divergent component of the velocity field. The Poisson equation used matches the electrostatic field equation, allowing a re-interpretation of the projection operation as a solution of electrostatic potential. Using a hierarchical dipole approximation, we achieve an efficient evaluation of the projection operator across sparse domains in a single pass. The update of each voxel is fully decoupled; allowing full parallelism and distribution.