Comparative Analysis of Three Smoothed Particle Hydrodynamics Methods in Modeling Free-surface Flows

摘要

Smoothed particle hydrodynamics (SPH) has been extensively applied in ocean/coastal engineering. In general, the SPH method can be divided into weakly compressible SPH (WCSPH) and incompressible SPH. The former is used more often than the latter because of its higher computational efficiency. The standard weakly compressible SPH has the issue of pressure fluctuations. Two typical WCSPH models developed to eliminate pressure fluctuations are the δ-SPH and Riemann-SPH models. The δ-SPH model introduces a diffusive term in the continuity equation, and Riemann-SPH uses a Riemann solver that determines the interaction between particles by a simple limiter to decrease the inherent numerical dissipation. In the present work, three models (standard-WCSPH, δ-SPH, and Riemann-SPH) are first considered to simulate the case of an oscillating drop as a classical free-surface flow benchmark. A comparison between the numerical simulation and theoretical solution on the time variation of energy and semimajor axis is conducted. The detailed pressure field is also discussed. Then test cases of violent sloshing and standing waves are conducted to further compare the three models. The numerical results are compared with available analytical and experimental data.