Smoothed Particle Hydrodynamics (SPH) Methods For Free Interfaces Of Fluids

The basic SPH(smoothed particle hydrodynamics) method was presented to numerically simulate a 2-D dam-break problem. On the basis of the original method, SPH is constantly being developed and revised, so this paper makes a comprehensive discussion on the recent development of the amendments, and by using the appropriate methods to simulate a 2-D underwater-rigid-landslide, the classic problems of free surface and large deformation, then we get better and more accurate data, and the availability and accuracy of the SPH method for the synthesis of the previous improved method in the large deformation free surface of the strongly nonlinear hydrodynamic problems are gradually verified, besides, the verified SPH method is used to simulate a single droplet and a square impact on liquid surface phenomenon which is very common in industrial problems. Using artificial viscosity which was developed by Monaghan to solve the initial shock effect, and artificial compression ratio which was proposed by Morris et al can make the fluid be weakly compressible. Moreover, we also use the repulsive force boundary conditions improved by Rogers to simulate the problem of dam-break, underwater-rigid-landslide, a droplet and a square impact free surface in two-dimensional, and analyzes in detail the whole process of waves and objects impact the surface. We track the particle at the surface or the objects, then we get the displacement and velocity of two particles with the time, so we can see the whole movement progress of the waves and the droplet shocking free surface clearly. At the same time, we compare the results of the boundary particles and the calculation process with the results of the grid method. The comparison shows that the SPH method has a unique advantage in dealing with the problem of free surface and large deformation.