ROE格式的物理增强图神经网络求解Euler与层流不可压NS方程

宋尚校; 姜龙祥; 王丽媛; 褚新坤; 张浩

doi:10.21656/1000-0887.450098

ROE格式的物理增强图神经网络求解Euler与层流不可压NS方程

doi: 10.21656/1000-0887.450098

中国工程物理研究院计算机应用研究所，四川绵阳 621900

详细信息

作者简介:
宋尚校(1996—)，男，助理工程师，硕士(E-mail: sshangxiao@126.com)

通讯作者:
张浩(1981—)，男，副研究员，博士(通讯作者. E-mail: linusec@163.com)

中图分类号: O29;O351
计量
- 文章访问数: 164
- HTML全文浏览量: 97
- PDF下载量: 34
- 被引次数: 0
出版历程
- 收稿日期: 2024-04-15
- 修回日期: 2024-07-08
- 刊出日期: 2025-01-01

ROE-Scheme Physics-Augmented Graph Neural Networks in Solving Eulerian and Laminar Flow Incompressible NS Equations

Institute of Computer Applications, China Academy of Engineering Physics, Mianyang, Sichuan 621900, P.R.China

摘要

摘要: 近年来，融合物理信息的深度学习方法为偏微分方程的求解提供了一个新的思路. 然而，到目前为止，大多数工作在解空间存在间断的问题上的计算精度不高，时间外推能力差. 针对以上两个问题，该文提出了使用图神经网络结合流体计算领域的ROE格式融合方程或数据信息的模型——ROE-PIGNN. 数值实验表明，该模型在求解由Euler方程控制的激波管问题时，可达到与传统ROE格式相当的计算精度，并具备一定时间范围的外推能力. 最后，对由Navier-Stokes(NS)方程控制的二维圆柱绕流问题进行了求解，实验结果表明：模型可以预测后续的周期性流动，并实现对部分关键位置流动结构的更精确的复现，相比纯数据驱动，误差降低了60%.
- 深度学习 /
- 图神经网络 /
- ROE格式 /
- Euler方程 /
- NS方程
Abstract: In recent years, the deep learning method incorporating physical information provided a new idea for solving partial differential equations. However, most of the studies so far has low computational accuracy and poor time extrapolation for problems with discontinuities in the solution space. To address the above 2 problems, the ROE-PIGNN model was proposed for fusing equations or data information with the graph neural networks and the ROE scheme in computational fluid dynamics. Numerical experiments show that, the model achieves a computational accuracy comparable to that of the ROE scheme in solving the shock tube problem controlled by the Eulerian equation, and has the ability of extrapolation over a certain time range. Finally, the 2D cylindrical bypass flow traditional problem controlled by the Navier-Stokes (NS) equations was solved. The experimental results show that, the model can predict the subsequent periodic flow and reproduce the flow structure more accurately at some key positions, with an error reduction of 60% compared to the purely data-driven approach.
- deep learning /
- graph neural network /
- ROE scheme /
- Eulerian equation /
- NS equation

HTML全文

图 1 ROE-PIGNN原理图

Figure 1. The ROE-PIGNN schematic diagram

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图 2 GNN架构

Figure 2. The graph neural network architecture

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图 3 SOD激波管问题中，以最小二乘法计算PDE损失的模型获得的压强p结果

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. Pressure results obtained for the model with PDE losses with the least squares method in the SOD shock tube problem

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图 4 SOD激波管问题中，以ROE格式计算PDE损失的模型获得的压强p结果

Figure 4. Pressure results obtained for the model with PDE losses in the ROE format for the SOD shock tube problem

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图 5 误差随时间变化的结果

Figure 5. Errors over time

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图 6 训练工况和时间外推下，模型计算压强场的结果

Figure 6. Results of the calculated pressure field for the model under training conditions and time extrapolation

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图 7 新初始场下，模型计算压强场的结果

Figure 7. Results of the calculated pressure field for the model with the new initial field

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图 8 误差随时间步的变化趋势

Figure 8. Trends of errors with the time step

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图 9 计算采用的网格的整体视图与局部视图

Figure 9. Overall and local views of the grid used for the calculation

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图 10 以PDE损失训练PIGNN在不同时刻的计算结果

Figure 10. Computational results of training PIGNN with PDE losses at different moments

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图 11 圆柱尾迹区添加数据损失的计算结果

Figure 11. Calculated results after adding data losses to the cylindrical wake area

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图 12 在少量的几个时刻添加数据损失的计算结果

Figure 12. Calculated results with data losses added at a small number of moments

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图 13 纯数据驱动和数据加方程驱动模型计算的尾迹区平均误差趋势

Figure 13. Trends of mean errors in the tailrace area calculated by purely data-driven and data-plus-equation-driven models

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