Dirichlet Boundary Conditions in Meshless Particle Methods for Free-Surface Flow Simulation under Negative Pressure Gradient

HAN Peidong; LIU Qixin; ZHOU Ziqi; SUN Zhongguo; XI Guang

doi:10.7652/xjtuxb202208015

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Dirichlet Boundary Conditions in Meshless Particle Methods for Free-Surface Flow Simulation under Negative Pressure Gradient

更新时间：2025-07-09

- Dirichlet Boundary Conditions in Meshless Particle Methods for Free-Surface Flow Simulation under Negative Pressure Gradient
- Vol. 56, Issue 8, Pages: 141-148(2022)
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202208015
  CLC： O351.2;TK730.2
- Online First：10 August 2022，
  
  Published：2022
- 稿件说明：
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HAN Peidong, LIU Qixin, ZHOU Ziqi, et al. Dirichlet Boundary Conditions in Meshless Particle Methods for Free-Surface Flow Simulation under Negative Pressure Gradient[J]. 2022, 56(8): 141-148.
DOI：

HAN Peidong, LIU Qixin, ZHOU Ziqi, et al. Dirichlet Boundary Conditions in Meshless Particle Methods for Free-Surface Flow Simulation under Negative Pressure Gradient[J]. 2022, 56(8): 141-148. DOI： 10.7652/xjtuxb202208015.

摘要

为改善无网格粒子法自由表面附近计算精度及稳定性

尤其在负压梯度条件下较难收敛的状况

提出了一种基于虚拟边界的狄利克雷边界条件赋值方法。以移动粒子半隐式法为例

采用最小二乘法对自由表面粒子进行多项式拟合

以拟合曲线作为虚拟边界

用自由表面粒子到虚拟边界的偏差矢量对自由表面粒子赋值进行修正。通过方形液滴旋转算例验证了算法的有效性与准确性

获得了自由表面平滑的模拟结果。进一步研究了关键参数的选择对边界条件的表达和计算精度的影响

发现当拟合搜索半径为4倍初始粒子间距时

可减小拟合误差

防止边界畸变。提出的改进方法提高了自由表面核截断区域的计算精度与稳定性

可显著改善负压梯度下大变形自由曲面外缘粒子因梯度力偏差而导致的粒子飘散情况

为改善大变形复杂界面流动计算提供了新的思路。

Abstract

Dirichlet boundary conditions for the free-surface are normally imposed through direct assignment in meshless particle methods. The discretization error caused by the disordered particle distribution is generally ignored. Since it is especially difficult to calculate convergence under the negative pressure gradient

to improve the calculation accuracy and stability near the free surface

this paper proposes a Dirichlet boundary condition assignment method based on the virtual boundary. Using the moving particle semi-implicit method

polynomial fitting is carried out for free-surface particles with the least square method. The fitting curve is taken as the virtual boundary

and the deviation vector from the free-surface particle to the virtual boundary is used to correct the assignment. The validity and accuracy of the algorithm are proved through the case of a rotating square patch of fluid. This paper also further studies the influence of the key parameters on the accuracy and manifestation of the boundary conditions. When the search radius for fitting is four times the initial interparticle distance

fitting errors can be reduced and boundary deformation can be prevented. The proposed method can enhance the accuracy and stability in the kernel truncation region of the free surface

and can significantly suppress the particle drift caused by gradient force deviation on the free surface

in case of large deformation and under a negative pressure gradient. This paper provides new thoughts for improving the flow calculation of complex interfaces with large deformation.

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references

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