The moving particle semi-implicit method (MPS) is a well-known Lagrange method that offers advantageous in addressing complex fluid problems, but particle distribution is an area that requires refinement. For this study, a particle smoothing algorithm was developed and incorporated into the weakly compressible MPS (sWC-MPS). From the definition and derivation of basic MPS operators, uniform particle distribution is critical to numerical accuracy. Within the framework of sWC-MPS, numerical operators were modified by implementing coordinate transformation and smoothing algorithm. Modifying numerical operators significantly improved particle clustering, smoothed pressure distributions, and reduced pressure oscillations. To validate the numerical feasibility of the method, several cases were numerically simulated to compare sWC-MPS to the weakly compressible MPS (WC-MPS): a pre-defined two-dimensional (2-D) analytical function, Poiseuille's flow, Taylor Green vortex, and dam break. The results showed a reduction of errors caused by irregular particle distribution with lower particle clustering and smaller pressure oscillation. In addition, a larger Courant number, which represents a larger time step, was tested. The results showed that the new sWC-MPS algorithm achieves numerical accuracy even using a larger Courant number, indicating improved computational efficiency.

移动粒子半隐式方法 (MPS) 是众所周知的拉格朗日方法，它在解决复杂的流体问题方面具有优势，但粒子分布是一个需要细化的领域。对于这项研究，开发了一种粒子平滑算法并将其合并到弱可压缩 MPS (sWC-MPS) 中。从基本 MPS 算子的定义和推导来看，均匀的粒子分布对数值精度至关重要。在 sWC-MPS 框架内，通过实现坐标变换和平滑算法来修改数值算子。修改数值算子可显着改善粒子聚类、平滑压力分布并减少压力振荡。为了验证该方法的数值可行性，对几种情况进行了数值模拟，以将 sWC-MPS 与弱可压缩 MPS (WC-MPS) 进行比较：预定义的二维 (2-D) 分析函数、泊肃叶流、泰勒格林涡流和大坝溃决。结果表明，由于颗粒分布不规则、颗粒聚集和压力振荡较小而导致的误差减少。此外，还测试了代表较大时间步长的较大 Courant 数。结果表明，即使使用更大的柯朗数，新的 sWC-MPS 算法也能达到数值精度，表明计算效率有所提高。结果表明，由于颗粒分布不规则、颗粒聚集和压力振荡较小而导致的误差减少。此外，还测试了代表较大时间步长的较大 Courant 数。结果表明，即使使用更大的柯朗数，新的 sWC-MPS 算法也能达到数值精度，表明计算效率有所提高。结果表明，由于颗粒分布不规则、颗粒聚集和压力振荡较小而导致的误差减少。此外，还测试了代表较大时间步长的较大 Courant 数。结果表明，即使使用更大的柯朗数，新的 sWC-MPS 算法也能达到数值精度，表明计算效率有所提高。