document: Traditionally, the simulation of incompressible fluid flow by the SPH method has been through a weakly compressible SPH formulation (WCSPH). In this approach, the pressure is treated as a thermodynamic variable and is calculated using an artificial equation of state. The sound speed is set to be sufficiently high to limit density variations to within a small fraction of the actual fluid density. In practice, this high sound speed places a limitation on the maximum permissible time-step size through the Courant–Friedrichs–Lewy (CFL) constraint. A particular weakness relates to noise in the pressure field since a small perturbation in the local density will yield a large variation in the local pressure. This can make WCSPH formulations ineffective for accurate force and pressure prediction, although recent developments which create more uniform particle distributions have improved this [1,2]. A review of the SPH method can be found in [3] while a review of the classical WCSPH formulation applied to free-surface flows can be found in [4].
extractive_keyphrases: artificial equation of state create more uniform particle distributions fluid sph method wcsph weakly compressible sph formulation
abstractive_keyphrases: fluid flow free-surface flows particle simulation of incompressible fluid flow