An SPH projection method

A new formulation is introduced for enforcing incompressibility in Smoothed particle Hydrodynamics (SPH). The method uses a fractional step with the v elocity field integrated forward in time without enforcing incompressibilit y. The resulting intermediate velocity held is then projected onto a diverg ence-free space by solving a pressure Poisson equation derived from an appr oximate pressure project-ion. Unlike earlier approaches used to simulate in compressible flows with SPH, the pressure is not a thermodynamic variable a nd the Courant condition is based only on fluid velocities and not on the s peed of sound. Although larger time-steps can be used, the solution of the resulting elliptic pressure Poisson equation increases the total work per t ime-step. Efficiency comparisons show that the projection method has a sign ificant potential to reduce the overall computational expense compared to w eakly compressible SPH, particularly as the Reynolds number, Re, is increas ed. Simulations using this SPH projection technique show good agreement wit h finite-difference solutions for a vortex spin-down and Rayleigh-Taylor in stability. The results, however, indicate that the use of an approximate pr ojection to enforce incompressibility leads to error accumulation in the de nsity held. (C) 1999 Acadamic Press.