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.

自适应粒子细化 (APR) 可以通过将母粒子拆分为更小的子粒子来提高无网格粒子方法的效率。然而，大多数 APR 算法都基于解决一个最小化问题，在这个问题中，单个母粒子被分裂成几个子粒子。这可能会导致精度不足，因为APR通常用于分裂涉及许多母粒子的问题，并且在相邻母粒子之间的细化误差场中可能出现叠加效应。因此，我们为基于直接分裂多个母粒子的平滑粒子流体动力学 (SPH) 方法开发了一种新的 APR 策略，以获得更准确的最佳 APR 参数。此外，推导出角动量守恒条件，并提出了一种新算法来实现明渠流的周期性边界条件。此外，我们首次进行了严格的参数研究，以研究影响最佳 APR 参数的因素，包括分裂模式、核类型、密度计算算法以及细化误差定义。此 APR 策略已通过五个基准测试用例进行验证。测试结果表明，所提算法在提高仿真精度、降低计算成本的同时，表现出良好的实现灵活性。密度计算算法以及细化误差定义。此 APR 策略已通过五个基准测试用例进行验证。测试结果表明，所提算法在提高仿真精度、降低计算成本的同时，表现出良好的实现灵活性。密度计算算法以及细化误差定义。此 APR 策略已通过五个基准测试用例进行验证。测试结果表明，所提算法在提高仿真精度、降低计算成本的同时，表现出良好的实现灵活性。