Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> III. THEORETICAL PROCESS OF SPH <s> The SPH (smoothed particle hydrodynamics) method is extended to deal with free surface incompressible flows. The method is easy to use, and examples will be given of its application to a breaking dam, a bore, the simulation of a wave maker, and the propagation of waves towards a beach. Arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles. The method is explicit, and the time steps are therefore much shorter than required by other less flexible methods, but it is robust and easy to program. <s> BIB001 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> III. THEORETICAL PROCESS OF SPH <s> We present a weakly compressible form of the Smoothed Particle Hydrodynamics method (SPH) for fluid flow based on the Tait equation. In contrast to commonly employed projection approaches that strictly enforce incompressibility, time-consuming solvers for the Poisson equation are avoided by allowing for small, user-defined density fluctuations. We also discuss an improved surface tension model that is particularly appropriate for single-phase free-surface flows. The proposed model is compared to existing models and experiments illustrate the accuracy of the approach for free surface flows. Combining the proposed methods, volume-preserving low-viscosity liquids can be efficiently simulated using SPH. The approach is appropriate for medium-scale and small-scale phenomena. Effects such as splashing and breaking waves are naturally handled. <s> BIB002
The simulation of incompressible fluid by SPH can be divided into two methods: weak compressible SPH (WCSPH) BIB002 , and incompressible SPH (ISPH). Monaghan BIB001 first applied the SPH to an incompressible free surface flow simulation. The traditional WCSPH is simpler than other methods because it uses the artificial state equation to explicitly correlate the fluid pressure with the local density. By choosing the appropriate equation of state to ensure that the Mach number is less than 0.1 in the flow process, flow is achieved in this approximation of incompressibility. Compared with WCSPH, ISPH is a semi-implicit approach whose pressure has a Poisson equation iterative solution to solve the velocity explicitly. The following two methods are introduced.