卷积自编码器在非定常可压缩流动降阶模型中的适用性

肖若冶; 于剑; 马正宵

doi:10.13700/j.bh.1001-5965.2022.0085

卷积自编码器在非定常可压缩流动降阶模型中的适用性

doi: 10.13700/j.bh.1001-5965.2022.0085

北京航空航天大学航空科学与工程学院，北京 100191

基金项目: 国家自然科学基金(11972064)；航空工业气动院计算空气动力学重点实验室基金 (YL2022XFX0405)

详细信息

通讯作者:
E-mail：yuj@buaa.edu.cn

中图分类号: V211.3
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- 被引次数: 0
出版历程
- 收稿日期: 2022-02-24
- 录用日期: 2022-05-27
- 网络出版日期: 2022-06-06
- 整期出版日期: 2023-12-29

Applicability of convolutional autoencoder in reduced-order model of unsteady compressible flows

School of Aeronautic Science and Engineering，Beihang University，Beijing 100191，China

Funds: National Natural Science Foundation of China (11972064); Key Laboratory of Computational Aerodynamics, AVIC Aerodynamics Research Institute Foundation (YL2022XFX0405)

More Information

Corresponding author: E-mail：yuj@buaa.edu.cn

摘要

摘要:
为有效降低使用计算流体力学(CFD)方法的设计成本和周期，降阶模型(ROM)得到广泛关注。对于复杂的可压缩流动，使用本征正交分解(POD)等线性方法进行流场降维，需要大量模态才能保证流场重建的精度，采用非线性降维方法能够有效减少所需模态数。卷积自编码器(CAE)是一种由编码器和解码器组成的神经网络，能够实现数据降维和重构，可看作是POD方法的非线性拓展。采用CAE进行流场数据的非线性降维，同时使用长短期记忆(LSTM)神经网络进行流场状态的时间演化。对于不可压缩问题，使用自编码器和LSTM结合进行流场重构的方法已有较多研究，选择一维Sod激波管、Shu-Osher问题、二维黎曼问题和开尔文-亥姆霍兹不稳定性算例，测试该ROM对非定常可压缩流动的有效性，同时基于POD方法，在不同模态数下构造Sod激波管和黎曼问题的ROM作为对比。结果表明：对于非定常可压缩流动，CAE-LSTM方法能够在使用较少自由变量数的前提下获得较高的重构和预测精度。
- 降阶模型 /
- 卷积自编码器 /
- 长短期记忆神经网络 /
- 非定常可压缩流动 /
- 流场重构
Abstract:
To effectively reduce the design cost and cycle time of using computational fluid dynamics (CFD) methods, the reduced-order model (ROM) has gained wide attention in recent years. For complex compressible flows, using linear methods such as proper orthogonal decomposition (POD) for flow field dimensionality reduction requires a large number of modes to ensure reconstruction accuracy. It has been shown that the mode number can be effectively reduced by using nonlinear dimensionality reduction methods. Convolutional autoencoder (CAE) is a neural network composed of the encoder and decoder, which can realize data dimensionality reduction and reconstruction, regarded as a nonlinear extension of POD method. CAE is used for nonlinear dimensionality reduction, and long short-term memory (LSTM) neural network is used for time evolution. To address flow incompressibility, the combination of Autoencoder and LSTM for flow field reconstruction has been extensively studied. We examine the one-dimensional Sod shock tube, Shu-Osher problem, two-dimensional Riemann problem and Kelvin-Helmholtz instability problem to test the validity of the ROM for unsteady compressible flows. The ROMs of Sod shock tube and Riemann problem are constructed based on POD by different modes for comparison. The results show that CAE-LSTM method can obtain high reconstruction and prediction accuracy on the premise of using less latents for unsteady compressible flows.
- reduced-order model /
- convolutional autoencoder /
- long short-term memory neural network /
- unsteady compressible flow /
- flow field reconstruction

HTML全文

图 1 POD方法分解和重构流场的过程

Figure 1. Process of decomposition and reconstruction of flow field by POD method

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图 2 多层自编码器

Figure 2. A multi-layer autoencoder

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图 3 卷积的工作原理

Figure 3. Principle of convolution

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图 4 极大池化

Figure 4. Max pooling

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图 5 向上采样

Figure 5. Up sampling

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图 6 CAE-LSTM网络的结构

Figure 6. Structure of CAE-LSTM

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图 7 Sod激波管流场的CAE重构

Figure 7. Reconstruction of Sod tube by CAE

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图 8 Sod激波管流场的POD重构

Figure 8. Reconstruction of Sod tube by POD

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图 9 Sod激波管流场的重构平均相对误差

Figure 9. MRE of Sod tube reconstruction

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图 10 Sod激波管流场的CAE-LSTM预测

Figure 10. Prediction of Sod tube by CAE-LSTM

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图 11 Sod激波管流场的POD-LSTM预测

Figure 11. Prediction of Sod tube by POD-LSTM

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图 12 Sod激波管流场的预测平均相对误差

Figure 12. MRE of Sod tube prediction

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图 13 Shu-Osher问题的流场预测

Figure 13. Prediction of Shu-Osher by CAE-LSTM

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图 14 Shu-Osher问题的流场重构和预测平均相对误差

Figure 14. MRE of Shu-Osher reconstruction and prediction

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图 15 二维黎曼问题的重构流场

Figure 15. Reconstruction of 2D Riemann problem

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图 16 二维黎曼问题的流场重构平均相对误差

Figure 16. Reconstruction MRE of 2D Riemann problem

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图 17 二维黎曼问题的预测流场

Figure 17. Prediction of 2D Riemann problem

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图 18 二维黎曼问题的流场预测误差

Figure 18. Prediction MRE of 2D Riemann problem

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图 19 KH不稳定性问题流场的初始条件^[31]

Figure 19. Initial condition of Kelvin–Helmholtz (KH) instability problem^[31]

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图 20 KH不稳定性问题流场的CAE-LSTM网络预测

Figure 20. Prediction of KH instability problem by CAE-LSTM

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图 21 KH不稳定性问题的流场重构和预测平均相对误差

Figure 21. MRE of reconstruction and prediction of KH instability problem

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