Adaptive particle refinement strategies in smoothed particle hydrodynamics

Adaptive particle refinement (APR) can increase the efficiency of mesh-free particle methods by splitting mother particles into smaller daughter particles. However, most APR algorithms are based on solving a minimization problem in which a single mother particle is split into several daughter particles. This may cause insufficient accuracy because APR is typically adopted in problems where many mother particles are involved in splitting, and a superposition effect may occur in the refinement error field between neighboring mother particles. Hence, we develop a novel APR strategy for the smoothed particle hydrodynamics (SPH) method based on direct splitting multiple mother particles to obtain more accurate optimal APR parameters. In addition, angular momentum conservation conditions are derived and a new algorithm is proposed to implement periodic boundary conditions for open-channel flows. Furthermore, for the first time, we conduct a rigorous parametric study to investigate factors affecting the optimal APR parameters, including the split patterns, kernel types, the density calculation algorithms as well as refinement error definitions. This APR strategy is validated through five benchmark test cases. Test results show that the proposed algorithm can both improve the simulation accuracy, reduce the computational cost and show good flexibility for implementation.