  A numerical method based on smoothed particle hydrodynamics with adaptive
spatial resolution (SPH-ASR) was developed for simulating free surface flows.
This method can reduce the computational demands while maintaining the
numerical accuracy. In this method, the spatial resolution changes adaptively
according to the distance to the free surface by numerical particle splitting
and merging. The particles are split for refinement when they are near the free
surface, while they are merged for coarsening when they are away from the free
surface. A search algorithm was implemented for identifying the particles at
the free surface. A particle shifting technique, considering variable smoothing
length, was introduced to improve the particle distribution. The presented
SPH-ASR method was validated by simulating various free surface flows, and the
results were compared to those obtained using SPH with uniform spatial
resolution (USR) and experimental data.
