The FPM, as a variant form of SPH, uses a set of auxiliary kernels for consistent interpolations of the basic unknown function and its spatial gradient, which can expel the boundary deficiency-induced errors. Acquisition of the auxiliary kernels is detailed, and their basic properties are discussed. The governing equations for motion of a particle system are derived in an alternative way based on the weak-form momentum equation. This approach is advantageous in easy treatment of free-surface boundary condition. For taking account of realistic viscosity effects in low Reynolds number flows, the Morris-type viscosity is implemented. A modified particle shift technology (PST) and a gradient-free artificial density diffusion technique are proposed for stabilizing the numerical scheme and for better solutions. Numerical examples are presented to demonstrate the effectiveness of the proposed PST and artificial density diffusion, as well as the capability and efficiency of the proposed numerical model in solving low and medium Reynolds number flow problems.

FPM作为SPH的一种变体形式，使用一组辅助核对基本未知函数及其空间梯度进行一致插值，可以消除边界缺陷引起的误差。详细介绍了辅助内核的获取，并讨论了它们的基本属性。粒子系统运动的控制方程是基于弱动量方程以另一种方式推导的。该方法的优点是易于处理自由表面边界条件。为了考虑低雷诺数流动中的实际粘度效应，采用莫里斯型粘度。提出了改进的粒子移位技术（PST）和无梯度人工密度扩散技术来稳定数值格式并获得更好的解决方案。数值例子证明了所提出的 PST 和人工密度扩散的有效性，以及所提出的数值模型在解决中低雷诺数流问题时的能力和效率。