基于机器学习的非定常流场网格自适应

李彩云; 安慰; 刘学军; 吕宏强

doi:10.7638/kqdlxxb-2022.0034

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基于机器学习的非定常流场网格自适应

研究论文 | 更新时间：2026-05-28

- 基于机器学习的非定常流场网格自适应
- Mesh adaptation for unsteady flow field based on machine learning
- 空气动力学学报 2023年41卷第6期页码：89-101
- 作者机构：
  
  1. 南京航空航天大学计算机科学与技术学院，模式分析与机器智能工业和信息化部重点实验室,南京,211106
  2. 南京航空航天大学航空学院,南京,210016
- 作者简介：
  
  李彩云（1997-），女，硕士研究生，研究方向：机器学习，网格自适应. E-mail：lcy_123@nuaa.edu.cn
  刘学军*（1976-），女，教授，研究方向：机器学习. E-mail：xuejun.liu@nuaa.edu.cn
- 基金信息：
  
  航空科学基金（2018ZA52002，2019ZA052011）;空气动力学国家重点实验室基金（SKLA20180102）;气动噪声控制重点实验室基金（ANCL20190103）
- DOI：10.7638/kqdlxxb-2022.0034
  中图分类号： TP181;V211.3
- 纸质出版：2023
- 稿件说明：
移动端阅览
李彩云, 安慰, 刘学军, 等. 基于机器学习的非定常流场网格自适应[J]. 空气动力学学报, 2023, 41(6): 89−101.

LI Caiyun, AN Wei, LIU Xuejun, et al. Mesh adaptation for unsteady flow field based on machine learning[J]. 2023, 41(6): 89-101.
李彩云, 安慰, 刘学军, 等. 基于机器学习的非定常流场网格自适应[J]. 空气动力学学报, 2023, 41(6): 89−101. DOI： 10.7638/kqdlxxb-2022.0034

LI Caiyun, AN Wei, LIU Xuejun, et al. Mesh adaptation for unsteady flow field based on machine learning[J]. 2023, 41(6): 89-101. DOI： 10.7638/kqdlxxb-2022.0034.

摘要

现有针对非定常流场数值模拟的网格自适应方法，通常每隔一段时间步就进行一次网格调整，增加了计算复杂度和精度损失。针对这一问题，本文基于间断伽辽金（discontinuity Galerkin

DG）有限元法提出了结合BPNN（backpropagation neural network）和MMPDE（moving mesh partial differential equation）的非定常流场网格自适应方法。该方法首先采用DG有限元法对Navier-Stokes方程进行非定常计算，得到统计意义上的网格间断量；然后以初始网格和间断量训练BPNN回归模型，用于预测任意位置节点的间断量；接着使用MMPDE变分法移动网格节点，使其符合统计意义的间断量分布；最终通过Laplacian网格平滑法保证网格单元质量。圆柱绕流非定常流场算例的验证结果表明，该方法能够在不改变网格拓扑结构和不增加节点数的情况下完成一次性网格自适应，显著提高了非定常流场数值计算的精度和效率。

Abstract

Existing grid adaptation methods for numerical simulation of unsteady flow fields usually perform grid adjustment every time step

which increases the computational complexity and the possibility of accuracy loss. In view of this

based on the DG finite element method

an MMPDE mesh adaptation method combined with BPNN is proposed for intelligent mesh optimization of unsteady flow fields. The method first uses the DG finite element method to solve the unsteady N-S equation and obtain the statistical grid discontinuity. Using the initial grid and grid discontinuity to train the BPNN regression model

the discontinuity value of any node at any position can be predicted. The variational method

MMPDE

is selected to move grid nodes to conform to the distribution of discontinuities. Finally

the Laplacian grid smoothing method improves the grid quality. The feasibility of the method is verified by cases of unsteady flow fields around cylinders. The calculation results show that the method can complete the one-time adaptive adjustment of the grid without changing the grid topology and the number of nodes

which can significantly improve the accuracy and efficiency of numerical simulations for unsteady flow fields.

关键词

Keywords

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