Truly incompressible SPH

The method of smoothed particle hydrodynamics (SPH) is extended to model moderate Re number incompressible flows by employing an approximate projection method to enforce incompressibility. The method uses a fractional step with the velocity field integrated forward in time without enforcing incompressibility. The resulting intermediate velocity field is then projected onto a divergence-free space by solving a pressure Poisson equation. Unlike the current approach to simulating incompressible flows in SPH, the use of a large sound speed is not required in this technique leading to significantly relaxed time-step constraint. However, the solution of an elliptic problem leads to an increase in the work per time step. Simulations using this SPH projection technique show close agreement with finite-difference solutions for a vortex spin-down and a Rayleigh-Taylor instability. The vortex spin-down results, however, indicate that the use of an approximate projection to enforce incompressibility will lead to error accumulation in the density field. Efficiency comparisons between it and the current SPH approach indicate the method's potential to significantly reduce the computational time of incompressible flow simulations using SPH, particularly as the Re number is increased.