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

An Initial Distribution Optimization Algorithm for Complex Boundaries Based on Numerical Integration for Particle Method

为提高粒子法研究中初场计算节点的空间分布质量,包括计算域内部计算节点分布的各向同性和计算域边界附近计算节点对理论边界的贴体性,提出了一种计算节点(即粒子)初场布置的优化方法。该方法借助网格控制求解域的边界,采用粒子迁移模型使流体粒子自适应地发展为均匀各向同性的分布状态。为了将网格的信息耦合进粒子法的粒子迁移模型中,在粒子迁移模型中引入了基于边界网格的数值积分算法。验证算例包括二维椭圆、二维转子泵、三维复杂腔体、三维球体等,验证结果表明:所提出的初场布置优化算法能够保证流体域内粒子的均匀各向同性分布,并减小边界粒子与理论边界的偏差值,降低边界粒子数密度的噪点;在液滴模拟中,优化初场布置后的圆度误差较传统初场布置减小了78.6%。

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.