An improved SPH approach for simulating 3D dam-break flows with breaking waves

In this article, we develop an improved smoothed particle hydrodynamics (SPH) approach for simulating 3D dam-break flows with breaking waves. In order to improve the computational accuracy and pressure distributions, the correction of kernel gradient and the introduction of Rusanov flux into the continuity equation are particularly implemented. Also, both wall and dummy particles are employed for modeling the complex solid boundaries in a flexible way. To show the ability of the improved SPH approach for solving 3D free surface flow problems, three challenging numerical examples including 3D dam-break flow against a vertical wall, against a cuboid obstacle, and against a cylindrical obstacle are numerically simulated and compared with available experimental data in literature. The convergent behavior of the numerical algorithm has also been studied by using different particle resolutions. It is demonstrated that the improved SPH approach is capable of handling with 3D free surface flows with large deformations and fragmentations accurately and stably, and even more important, also computing an accurate and fluctuations-free pressure field.