A Particle Rearrangement Approach for Optimizing Planar and Surface Particle Distributions in Meshless Particle Methods

Particle-based meshless methods are commonly used in fluid dynamics and solid mechanics involving finite deformations, owing to their ability to break through the limitations imposed by mesh topology. Particle distribution usually plays a crucial role in determining the accuracy of simulation results for them. In this study, an error estimation was first conducted to ascertain the requirements for particle distribution necessary for accurate simulations. It was revealed that the sawtooth and chaotic particle distributions can significantly reduce numerical accuracy and even cause numerical instability in simulations. To address this issue, we propose a particle rearrangement approach including a pseudo hydrostatic pressure treatment to achieve body-fitted particles and a geometric smoothing method based on the metric of a point cloud unit to optimize chaotic particle distributions for improved regularity. The particles are iteratively moved according to their proximity to neighboring particles. Notably, the number of particles remains constant throughout the smoothing procedure, neither particles inserted or removed, nor particles overflow or volume expansion. This new approach facilitates the generation of body-fitted and relatively regular planar and surface particle distributions, meeting the requirements for arbitrarily complex shape particle distributions. The effectiveness of this method has been demonstrated through two-dimensional SPH simulations for problems of the flow around a cylinder, dam break, and Taylor–Green vortex.