Compressible cavity flows exist widely in aeronautical vehicles. The cost of the computational fluid dynamics to solve compressible cavity flows is high. To address this issue, in this work, a novel reduced-order model (ROM) combining proper orthogonal decomposition (POD) with the long short-term memory (LSTM) neural network named LSTM-ROM for predicting the compressible cavity flows is proposed. First, POD is used to provide a low-dimensional subspace. Then, the LSTM neural network is designed to predict the POD coefficients with time evolution. The results show that the LSTM-ROM can accurately predict the POD coefficients for a long time and capture the shock wave structures at supersonic speed. The predicted density and normal velocity field are consistent with those simulated by direct numerical simulation (DNS). The calculation time of LSTM-ROM is almost one-seventh of that of DNS. By comparing the performance of LSTM-ROM with that of dynamic mode decomposition (DMD) and multilayer perceptron (MLP), it is found that the root mean square errors of density and normal velocity field predicted by LSTM-ROM are smaller than those predicted by DMD and MLP. In addition, the LSTM-ROM can accurately and efficiently predict the flows over cavities with different inclination angles at subsonic speed. Therefore, the LSTM-ROM is an accurate and efficient method for predicting the compressible cavity flows, which lays a foundation for other complex flows.

可压缩腔流广泛存在于航空飞行器中。求解可压缩腔体流动的计算流体动力学成本很高。为了解决这个问题，在这项工作中，提出了一种新的降阶模型 (ROM)，将适当的正交分解 (POD) 与名为 LSTM-ROM 的长短期记忆 (LSTM) 神经网络相结合，用于预测可压缩腔体流动。首先，POD 用于提供一个低维子空间。然后，设计 LSTM 神经网络来预测 POD 系数随时间演化。结果表明，LSTM-ROM可以长时间准确地预测POD系数，并能以超音速捕捉冲击波结构。预测的密度和法向速度场与直接数值模拟（DNS）模拟的一致。LSTM-ROM的计算时间几乎是DNS的七分之一。通过比较 LSTM-ROM 与动态模式分解 (DMD) 和多层感知器 (MLP) 的性能，发现 LSTM-ROM 预测的密度和法向速度场的均方根误差小于DMD 和 MLP。此外，LSTM-ROM 可以准确有效地预测亚音速下具有不同倾角的腔体的流动。因此，LSTM-ROM 是一种准确有效的预测可压缩腔流动的方法，为其他复杂流动奠定了基础。发现LSTM-ROM预测的密度和法向速度场的均方根误差小于DMD和MLP预测的。此外，LSTM-ROM 可以准确有效地预测亚音速下具有不同倾角的腔体的流动。因此，LSTM-ROM 是一种准确有效的预测可压缩腔流动的方法，为其他复杂流动奠定了基础。发现LSTM-ROM预测的密度和法向速度场的均方根误差小于DMD和MLP预测的。此外，LSTM-ROM 可以准确有效地预测亚音速下具有不同倾角的腔体的流动。因此，LSTM-ROM 是一种准确有效的预测可压缩腔流动的方法，为其他复杂流动奠定了基础。