发表机构
Karlsruhe Institute of Technology; University of Rostock（卡尔斯鲁厄理工学院; 罗斯托克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出有限体积卷积单元（FVCU），将CNN超分辨率框架扩展至通用有限体积网格，实现非均匀/非正交网格下壁面湍流的精细尺度重建，在多种流动构型中表现良好。
AI 中文摘要
用于湍流超分辨率的标准卷积神经网络（CNN）受限于均匀结构化网格，无法直接应用于壁面流动及复杂几何中常用的非均匀、非正交网格。本文提出一种有限体积卷积单元（FVCU），消除了这一限制。核心思路是采用适用于非均匀、非结构化网格的有限体积算子构建卷积层，具体将三维卷积精确表示为逐轴连续卷积的线性组合，采用可通过有限体积离散化在任意多面体单元上计算的逐轴梯度、平均及恒等算子。所得FVCU可在通用网格上精确定义，可直接替代传统卷积层。将FVCU嵌入超分辨率神经网络，在非均匀网格的湍流通道流、非正交O型网格的圆管流中，训练其从4倍粗化的低分辨率场重建三维速度场；受大涡模拟近壁亚格子尺度建模中Van Driest阻尼函数的启发，将该函数作为条件输入编码壁面邻近信息，消融实验证实网络以物理一致的方式解读该输入。在两种构型中，模型可精确重建瞬时速度场、雷诺应力及其各向异性，以及超出低分辨率网格奈奎斯特极限的能谱；在训练时未见过的椭圆管中，模型重现了主要流动特征与局部统计量，仅小幅高估小尺度能量。这些结果证明了将基于CNN的超分辨率扩展到通用有限体积网格的框架可行性。
英文摘要
Standard convolutional neural networks for turbulence super-resolution are restricted to uniform structured grids, preventing their direct application to the non-uniform and non-orthogonal meshes commonly used in wall-bounded flows and complex geometries. We introduce a finite-volume convolution unit (FVCU) that removes this restriction. The key idea is to construct convolutional layers using finite-volume operators that are applicable to non-uniform and unstructured meshes. To this end, we use an exact representation of a 3D convolution as a linear combination of successive axis-wise convolutions. We adopt axis-wise gradient, averaging, and identity operators, as they can be evaluated on arbitrary polyhedral cells using finite-volume discretization. The resulting FVCU is well-defined on general meshes, serving as a drop-in replacement for conventional convolution layers. The FVCU is embedded in a super-resolution neural network and trained to reconstruct 3D velocity fields from $4\times$ coarsened low-resolution fields in turbulent channel flow on a non-uniform mesh, and in circular-pipe flow on a non-orthogonal O-grid mesh. Inspired by the role of the Van Driest damping function in near-wall subgrid-scale modelling in large-eddy simulations, this function is supplied as a conditional input to encode wall proximity. An ablation study confirms that the network interprets this input in a physically consistent manner. In both configurations, the model accurately reconstructs instantaneous velocity fields, Reynolds-stresses and their anisotropy, and energy spectra beyond the Nyquist limit of the low-resolution mesh. On an elliptic pipe unseen during training, the model reproduces the main flow features and local statistics, with a modest overprediction of small-scale energy. These results demonstrate a framework for extending CNN-based super-resolution to general finite-volume grids.
