发表机构
University of Macau; Huazhong University of Science and Technology; Chinese Academy of Sciences; Sun Yat-Sen University; Tsinghua University; Zhuhai UM Science and Technology Research Institute（澳门大学; 华中科技大学; 中国科学院; 中山大学; 清华大学; 珠海UM科学技术研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种混合POD-自编码器降阶建模框架，通过按时间特征分解流场并分别预测，在雷诺数110的湍流槽道流中实现更准确稳健的长期统计预测。
AI 中文摘要
本研究提出了一种用于湍流模拟的混合降阶建模（ROM）框架。其核心思想是根据时间特征对流动动力学进行分解，并分别预测各组成部分。首先将整个流场划分为由有限数量的本征正交分解（POD）模态表示的子场（称为POD保留场）和相应的残差子场（称为POD截断场）。一种频率感知的POD策略通过同时考虑模态能量和主频率来识别保留模态。保留的POD系数具有相似的时间尺度，其演化采用向量自回归（VAR）模型描述。与此同时，POD截断场通过基于傅里叶神经算子的Koopman β-变分自编码器（FK-β-VAE）压缩到低维潜空间，随后潜变量由切换VAR模型预测。通过组合两个分量的贡献来恢复整个流场的湍流统计量。该框架在摩擦雷诺数为110的湍流槽道流中进行了评估。预测的雷诺应力分量、湍动能（TKE）和主波数谱与参考结果吻合良好。此外，与全流场建模（即不进行场分解）的替代框架相比，所提出的框架产生了更准确和稳健的长期统计预测。
英文摘要
This study proposes a hybrid reduced-order modeling (ROM) framework for the simulation of turbulent flow. The central idea is to decompose flow dynamics according to their temporal characteristics and predict the resulting components individually. The full field is first divided into a sub-field represented by a limited number of proper orthogonal decomposition (POD) modes (named as POD-retained field) and the corresponding residual sub-field (named as POD-truncated field). A frequency-informed POD strategy identifies the retained modes by considering both modal energy and dominant frequency. The evolution of retained POD coefficients, which feature similar temporal scales, is described using a vector autoregressive (VAR) model. In parallel, the POD-truncated field is compressed into a low-dimensional latent space using a Fourier-neural-operator-based Koopman $β$-variational autoencoder (FK-$β$-VAE), with the latent variables subsequently predicted by a switching-VAR model. Turbulent statistics of the full field are recovered by combining the contributions from the two components. The framework is assessed using turbulent channel flow at a friction Reynolds number of $110$. The predicted Reynolds-stress components, turbulent kinetic energy (TKE), and dominant wavenumber spectra show good agreement with the reference. Moreover, in comparison with an alternative framework of full-field modeling (i.e., without field decomposition), the proposed framework yields more accurate and robust long-term statistical predictions.
