AI 中文总结
研究壁面湍流建模，提出可微混合神经 - 计算流体动力学框架，联合学习亚格子尺度和壁面边界条件，在可微流求解器中以低阶统计量为目标训练。模型性能优于基线，能外推、转移，消融研究验证联合优化必要性，训练后封闭可复用。
AI 中文摘要
壁面模型大涡模拟（WMLES）将亚格子尺度（SGS）封闭、壁面边界条件和数值离散化视为独立组件，但其效果通过相同的解析场耦合。本文提出了一种可微混合神经 - 计算流体动力学框架，其中SGS和壁面边界条件在可微流求解器中联合、端到端学习，仅使用低阶统计量作为训练目标。每个封闭都是一个组合神经算子，通过后验测试在Re_θ = 600 - 6500、计算域和网格分辨率上展示了该框架（Hybrid - Joint）。该模型优于WMLES基线，能外推到超过最高训练雷诺数四倍的情况，并能转移到训练中未出现的网格和域。消融研究表明单独学习任一封闭是不够的，只有联合优化才能恢复完整统计量。训练后的封闭可在所有情况下重复使用而无需重新训练。
英文摘要
Wall-modelled large-eddy simulation (WMLES) treats the subgrid-scale (SGS) closure, wall closure and numerical discretization as independent components, although their effects are coupled through the same resolved field. We present a differentiable hybrid neural--CFD framework in which the SGS and wall closures are learned jointly, end-to-end, within a differentiable flow solver, using only low-order statistics as training targets. Each closure is a composed neural operator: a trainable neural network followed by a fixed differentiable layer that preserves the structure of its conventional counterpart, so that the network learns only the functions left undetermined by the conventional form. Because every operation is differentiable, gradients of the training loss are back-propagated through the coupled solver, allowing both neural closures to be optimized consistently against the flow field, rather than fitted offline or in isolation. We demonstrate the framework, denoted Hybrid-Joint, on a zero-pressure-gradient turbulent boundary layer across a posteriori tests spanning Re_θ= 600--6500, computational domains and mesh resolutions. The model outperforms WMLES baselines, extrapolates to more than four times the highest training Reynolds number, and transfers to grids and domains absent from training. It recovers a logarithmic mean-velocity region, not imposed by the wall closure, and reproduces the resolved energy spectra accurately, although spectral information is excluded from the training objective. Ablation studies show that learning either closure alone is insufficient and that only joint optimization recovers the full set of statistics, confirming that SGS closure, wall closure and discretization are coupled and must be trained jointly. Once trained, the closures are reused without retraining across all cases, so that training cost is amortized over repeated deployment.
Comments39 pages, 22 figures
