一种适用于复杂边界的粒子法数值积分初始布置优化算法

To improve the quality of the spatial distribution of the initial field computational points in the particle method, including the isotropic distribution of inner particles within the computational domain as well as the fitting of the computational points near the boundaries of the computational domain to the theoretical boundaries, a method to optimize the initial distribution of computational points (namely particles) is proposed. The boundary meshes is applied to control the profiles of the computational domain. Additionally, the particle shifting model is applied to drive the particles to move spontaneously to form uniform isotropic distribution. In order to couple the mesh information with the particle shifting model used by the particle method, the numerical integration algorithm based on the boundary meshes is introduced into the particle shifting model. The validation cases include a two-dimensional ellipse, a two-dimensional rotor pump, a three-dimensional complex cavity, and a three-dimensional sphere. The results showed that by the proposed initial distribution optimization method, the uniform isotropic distribution of particles in the fluid domain can be ensured, the deviation of boundary particles from the theoretical boundary can be reduced, and the noise of the number density of boundary particles can be lowered. In the droplet simulation, the roundness error after the initial distribution optimization reduces by 78. 6% compared to the traditional initial distribution.