AI 中文总结
研究通过基于物理信息神经网络训练湍流封闭，无需在优化循环中使用CFD求解器，可快速筛选封闭形式。开发四种封闭模型，在多个钝体尾流中训练并评估，结果优于稳态SST k-ω基线，力模型泛化性最佳。
AI 中文摘要
数据驱动的湍流封闭通常通过逆方法校准，将CFD求解器置于优化循环中，使学习模型与特定离散化相关联且要求每次中间迭代收敛。我们改为在物理信息神经网络（PINN）中训练封闭：通过自动微分施加RANS残差，使逆问题无网格、可微且与求解器无关。训练时无需正向求解，仅最终封闭需求解器稳定，可接纳任意神经封闭而无需推导伴随式，避免迭代求解器成本。每个本构假设在单个GPU上几分钟内即可训练完成，实现封闭形式的快速筛选。我们开发了四种封闭：三种在张量基础上模拟雷诺应力并具有内置可实现性（局部映射、传输湍动能的非局部模型以及具有学习长度尺度l的相同模型），而第四种直接模拟雷诺力F = -∇·τ，无可实现性约束。这些封闭在Re = 10^4的六个二维钝体尾流中进行训练，并在有限元求解器中冻结部署。通过输入梯度平滑和Lipschitz约束增强耦合稳定性。我们在样本内和严格的留一形状（LOSO）协议下评估封闭。所有四种封闭在稳态SST k-ω基线上都有显著改进。学习长度尺度应力封闭在应力场上最准确，而传输动能对泛化起决定性作用。值得注意的是，力模型泛化性最佳，在平均速度和阻力上的样本外误差最低（LOSO阻力误差约8.5%）。最后，我们表明这些封闭可以在PIV数据上高效训练，实现对DNS难以处理的几何形状的数据驱动建模。
英文摘要
Data-driven turbulence closures are usually calibrated by inverse methods that embed a CFD solver in the loop, tying the model to a particular discretization and requiring every iterate to yield a convergent solve. We instead train the closure inside a physics-informed neural network (PINN): the Reynolds-averaged Navier-Stokes residual is imposed by automatic differentiation, so the inverse problem is mesh-free, differentiable, and solver-agnostic. Because no forward solve runs during training, only the final closure need be solver-stable, arbitrary neural closures are admitted without an adjoint, and the iterative cost of adjoint or ensemble methods vanishes; each hypothesis trains in minutes on a single GPU, so the framework rapidly screens closure forms. We develop four closures: three model the Reynolds stress on a realizable tensor basis -- a local map, a non-local model transporting the turbulent kinetic energy and recovering the out-of-plane normal stress, and the same with a learned length scale l -- and a fourth models the Reynolds force F = -\nabla \cdot τdirectly, free of the realizability constraint. All four are trained across six two-dimensional bluff-body wakes at Re = 10^4 and deployed frozen in a standard finite-element solver, stabilized by input-gradient smoothing and a Lipschitz constraint. Under a strict leave-one-shape-out (LOSO) protocol, all four improve substantially on a steady SST k-omega baseline. The learned-length-scale closure is most accurate on the stress fields, while the force model generalizes best on the mean velocity and drag (LOSO drag error ~8.5%). The closures also train efficiently on Particle Image Velocimetry data, enabling geometries intractable for DNS.
Comments42 pages, 24 figures
