Computing a null divergence velocity field using smoothed particle hydrodynamics

A new use of smoothed particle hydrodynamics (SPH) in fluid simulation is presented: an algorithm solving the Helmholtz-Hodge decomposition using SPH in order to find the null divergence velocity field for incompressible flow simulation. Accordingly, a new version of the Laplacian for a vector field is proposed here. In order to improve the accuracy of the SPH technique, the paper also presents some test problems for understanding the limitations of different kinds of gradient and Laplacian approximation formulas.