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基于速度修正的固壁边界处理方法

  

  1. (合肥工业大学数学学院,安徽 合肥 230009)
  • 出版日期:2019-08-31 发布日期:2019-08-30
  • 基金资助:
    国家自然科学基金项目(61272024)

Treatment of Solid Boundary Based on Velocity Correction

  1. (School of Mathematics, Hefei University of Technology, Hefei Anhui 230009, China)
  • Online:2019-08-31 Published:2019-08-30

摘要: 摘 要:固壁边界处理方法的研究一直是流体模拟中的难点问题,常见的固壁边界处理方 法有边界力法和虚粒子法。边界力法通过对靠近边界的流体粒子施加作用力防止其穿透边界, 但模型参数较多,力的大小难以调控,且在计算中会产生边界截断误差问题;虚粒子法通过在 边界外生成虚粒子解决了边界截断误差问题,但在处理复杂边界问题时,由于外部的虚粒子的 生成较困难,且分布不均,计算精度受到影响,出现粒子飞散的情况。针对 2 种方法存在的问 题,提出一种基于速度修正的固壁边界处理方法,无需求解边界力或在边界外生成虚粒子,直 接利用动量方程和计算速度耗损量求出流体粒子碰到边界后的反弹速度,大大降低了处理边界 的复杂程度,也克服了 2 种方法在边界拐角处粒子不均匀采样而导致的算法不稳定的问题。模 拟仿真验证了该方法在稳定性、计算效率方面均较传统边界力法和虚粒子法更好;随着粒子数 的增加,该方法耗时更少、计算效率更高,对复杂场景的模拟效果更好。

关键词: 关 键 词:流体模拟, 固壁边界, 边界力法, 虚粒子法, 速度修正

Abstract: Abstract: The study of solid boundary treatment method has been a difficult problem in fluid simulation. The common methods of solid boundary treatment are boundary force method and virtual particle method. The boundary force method prevents fluid particles from penetrating the boundary by exerting force on the fluid particles near the boundary, but this method has too many parameters and the force is difficult to adjust, and the boundary truncation error will occur in the calculation. The virtual particle method solves the problem of boundary truncation error by generating virtual particles outside the boundary. However, when dealing with complex boundary problems, the generation of virtual particles is difficult, and the calculation accuracy will be affected due to the uneven distribution of virtual particles, which leads to particles to disperse. To solve these problems, the paper presents a new method for the treatment of solid boundary based on velocity correction, which does not need to solve the boundary force or generate virtual particles outside the boundary. The momentum equation and the velocity consumption are used directly to calculate the rebound velocity of the fluid particles when they hit the boundary, which greatly reduces the complexity of the boundary treatment. It also overcomes the problem of the instability of the boundary force method and the virtual particle method caused by the uneven sampling of particles at the corner of the boundary. Simulation results show that the proposed method is more stable and more efficient than traditional methods above, and with the increase of the number of particles, the time consuming of this method is also slower than that of the two methods, and the advantage of high computational efficiency is more obvious and the simulation effect of complex scene is also better.

Key words: Keywords: fluid simulation, solid boundary, boundary force method, virtual particle method, velocity correction