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。
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.
作者
肖若冶
于剑
马正宵
XIAO Ruoye;YU Jian;MA Zhengxiao(School of Aeronautic Science and Engineering,Beihang University,Beijing 100191,China)
出处
《北京航空航天大学学报》
EI
CAS
CSCD
北大核心
2023年第12期3445-3455,共11页
Journal of Beijing University of Aeronautics and Astronautics
基金
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)。
关键词
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
reduced-order model
convolutional autoencoder
long short-term memory neural network
unsteady compressible flow
flow field reconstruction
