Application of particle splitting method for both hydrostatic and hydrodynamic cases in SPH

Smoothed particle hydrodynamics (SPH) method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid-solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse (mother) particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process, conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.