Divergence-Free SPH Fluid Simulation Using Density Constraint Condition

Abstract

In this paper, a novel, incompressible fluid simulation framework based on the divergence-free Smoothed Particle Hydrodynamics model is presented. The novel SPH model combines a system of non-linear density constraint conditions and the divergence-free velocity field condition to enforce fluid incompressibility. In the new framework, the position of particles is firstly modified by solving the density constraints, and the distribution of particles is adjusted to keep the density of fluid in a relatively constant state. Then the divergence-free state increases the stability significantly and reduces the number of solver iterations. Compared to the modern Smoothed Particle Hydrodynamic (SPH) solvers, the new SPH framework allows better incompressibility and similar convergence. Finally, the method of pre-computed smoothing kernel functions is used to accelerate the proposed SPH model. It can effectively improve the real-time performance of the algorithm while maintaining sufficient accuracy.