一种基于物理辅助深度神经网络的封闭框架，用于具有振动非平衡的可压缩流中的速度梯度动力学
A physics-assisted deep neural network-based closure framework for velocity gradient dynamics in compressible flows with vibrational non-equilibrium
浏览论文内容
中文总结 AI 辅助
研究针对具有振动非平衡的可压缩湍流中速度梯度演化，用物理辅助深度神经网络提出动力学模型，结合唯象学与数据驱动表示，构建H - EHEE模型，该模型相比现有模型有显著改进，与DNS数据一致性好。
中文摘要 AI 辅助
在本研究中，我们使用物理辅助深度神经网络为具有振动非平衡效应的可压缩湍流中的速度梯度演化提出了一个动力学模型。此类模型为理解与小尺度结构相关的非线性物理提供了一个强大的框架。在可压缩流中，热力学场对速度梯度动力学的影响通过热力学梯度场（TGF）张量来表示。TGF张量是速度梯度演化方程中的主要未封闭项之一。TGF张量包括压力 - 海森张量$\rho\boldsymbol{H}$和斜压张量$\boldsymbol{B}$的贡献。因此，所提出的框架纳入了$\boldsymbol{H}$和$\boldsymbol{B}$张量动力学的封闭。基于现有的关于$\boldsymbol{H}$张量控制机制的唯象学封闭，我们开发了一个基于神经网络的封闭，用于负责生成$\boldsymbol{B}$张量的无粘机制。与其他最近使用的张量基不同，本工作采用了一种新颖的张量基，允许在模型中纳入非对称特征。该框架还纳入了一个数据驱动的振动非平衡封闭。由此产生的框架结合了各种$\boldsymbol{H}$和$\boldsymbol{B}$张量控制机制的唯象学和数据驱动表示，称为混合增强均匀化欧拉方程（H - EHEE）模型。在一系列湍流马赫数下评估了模型预测，并与直接数值模拟（DNS）数据和现有的可压缩速度梯度模型进行了比较。H - EHEE模型与DNS统计数据显示出密切的一致性，并比现有模型有显著改进，特别是在高可压缩流区域。
英文摘要
In this study, we propose a dynamical model for the evolution of velocity gradients in compressible turbulent flows with vibrational non-equilibrium effects, using physics-assisted deep neural networks. Such models provide a powerful framework for understanding the nonlinear physics associated with small-scale structures. In compressible flows, the influence of thermodynamic fields on velocity-gradient dynamics is represented through thermodynamic gradient field (TGF) tensor. The TGF tensor is one of the primary unclosed terms in velocity-gradient evolution equations. The TGF tensor comprises contributions from the pressure-Hessian tensor, $ρ\boldsymbol{H}$, and the baroclinic tensor, $\boldsymbol{B}$. Accordingly, the proposed framework incorporates closures for both $\boldsymbol{H}$ and $\boldsymbol{B}$ tensor dynamics. Building upon existing phenomenological closures for the $\boldsymbol{H}$ tensor governing mechanisms, we develop a neural-network-based closure for the inviscid mechanism responsible for generating the $\boldsymbol{B}$ tensor. Unlike the other recently used tensor bases, the presented work employs a novel tensor basis allowing for the inclusion of non-symmetric features in the model. The framework also incorporates a data-driven closure for vibrational non-equilibrium effects.The resulting framework combines phenomenological and data-driven representations of various $\boldsymbol{H}$ and $\boldsymbol{B}$ tensors governing mechanisms, termed as the \textit{hybrid enhanced homogenized Euler equation} (H-EHEE) model. Model predictions are evaluated across a range of turbulent Mach numbers and compared against direct numerical simulation (DNS) data and existing compressible velocity-gradient models. The H-EHEE model exhibits close agreement with DNS statistics and provides significant improvements over existing models, particularly in highly compressible flow regimes.
