发表机构
Centrum Wiskunde & Informatica; University College London; University of Twente（数学与计算机科学中心; 伦敦大学学院; 特温特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对LBM湍流模拟，提出基于Tau-正交和线性回归的降阶亚格子闭合模型，在粗网格通道流中稳定复现参考统计，成本降低40倍。
AI 中文摘要
湍流流动跨越广泛的尺度范围，这使得在高雷诺数下直接数值模拟（DNS）的成本高得令人望而却步。大涡模拟（LES）通过仅解析大尺度运动提供了一种实用的替代方案，但其精度依赖于亚格子（SGS）模型。我们将Tau-正交（TO）框架引入格子玻尔兹曼方法（LBM），并使用宏观速度强迫。TO方法将建模目标从高维SGS场转移到一小部分空间积分量（QoIs）的时间动力学。训练数据通过预测-校正跟踪程序生成，该程序将粗网格模拟推向参考QoI轨迹。具有随机多元高斯残差的轻量级线性回归模型（LRS）随后自主驱动LES。紧凑的基于卷积的核替代了原始公式中的尖锐傅里叶滤波器，消除了其对矩形周期域的限制。我们首先在二维Kolmogorov流上评估该闭合模型，其中TO-LRS产生了稳定、统计准确的在线LES。然而，在解场中观察到有界的高频振荡。决定性的测试是三维湍流通道流，其每个方向的网格都比高保真参考粗五倍。在此情况下，普通BGK求解器不稳定，甚至经过校准的Smagorinsky和WALE模型也会过度耗散近壁流动。TO-LRS在涡粘性基底上应用，并通过平均剖面QoIs扩充QoI集合，重现了参考分布，并保持了DNS平均速度剖面，其每模拟时间单位的在线成本比高保真模拟低40倍。这些结果表明，基于QoI的降阶闭合模型是LBM中高维神经SGS模型的一种可解释且廉价的替代方案。
英文摘要
Turbulent flows span a wide range of scales, making direct numerical simulation (DNS) prohibitively expensive at high Reynolds numbers. Large eddy simulation (LES) offers a pragmatic alternative by only resolving the large-scale motions, but its accuracy hinges on the subgrid-scale (SGS) model. We introduce the Tau-orthogonal (TO) framework to the lattice Boltzmann method (LBM) using a macroscopic-velocity forcing. The TO method shifts the modeling target from a high-dimensional SGS field to the time dynamics of a small set of spatially integrated quantities of interest (QoIs). Training data are generated by a predictor-corrector tracking procedure that nudges coarse simulations toward reference QoI trajectories. Lightweight linear regression models with stochastic, multivariate Gaussian residuals (LRS) then drive the LES autonomously. Compact convolution-based kernels replace the sharp Fourier filters of the original formulation, lifting its restriction to rectangular periodic domains. We first evaluate the closure on two-dimensional Kolmogorov flow, where TO-LRS yields stable, statistically accurate online LES. However, bounded high-frequency oscillations are observed in the solution fields. The decisive test is three-dimensional turbulent channel flow, simulated on a grid five times coarser in every direction than the high-fidelity reference. Here the plain BGK solver is unstable, and even calibrated Smagorinsky and WALE models over-dissipate the near-wall flow. TO-LRS, applied on top of an eddy-viscosity substrate and with the QoI set augmented by mean-profile QoIs, reproduces the reference distributions and holds the DNS mean velocity profile, at $40\times$ lower online cost per simulated time unit than the high-fidelity simulation. These results establish reduced, QoI-based closures as an interpretable and inexpensive alternative to high-dimensional neural SGS models for LBM.
