动态降阶数据同化：基于稀疏速度测量

中文摘要 AI 辅助

我们提出了一种新颖的降阶数据同化框架，称为降阶动力学同化（RODAS），用于从稀疏速度测量中重建高分辨率、时间分辨的流场。该方法将低维实验观测与基于物理的参数化降阶模型相结合，从而能够实现测量区域之外的空间外推和时间超分辨率。该方法首先通过动态模态分解（DMD）从稀疏测量中识别主导动力学，随后通过将识别出的动力学投影到由高保真数值模拟生成的参数化本征正交分解（POD）流形上，重建相应的全阶流动演化。与传统的降阶数据同化方法（这些方法估计独立的快照或将时间视为附加参数）不同，RODAS在单次推断步骤中重建整个动力学轨迹，同时自然地纳入参数变异性。我们针对牛顿流体和非牛顿（Carreau-Yasuda）流体在圆柱体后的涡脱落对该方法进行了评估。数值实验表明，该方法能够从局部、低分辨率测量中准确重建高分辨率速度场，在足够丰富的降阶基下实现亚百分之一的重建误差，在严重时间欠采样下具有稳健性能，并能准确预测工程关注量（如阻力系数）。这些结果表明，RODAS为从稀疏实验数据实时、基于物理地重建非定常流动提供了一种高效框架。

英文摘要

We present a novel reduced-order data assimilation framework, termed Reduced-Order Dynamical Assimilation (RODAS), for reconstructing high-resolution, time-resolved flow fields from sparse velocity measurements. The method combines low-dimensional experimental observations with a physics-based parametric reduced-order model, enabling both spatial extrapolation beyond the measurement region and temporal super-resolution. The approach first identifies the dominant dynamics from sparse measurements through Dynamic Mode Decomposition (DMD), and subsequently reconstructs the corresponding full-order flow evolution by projecting the identified dynamics onto a parametric Proper Orthogonal Decomposition (POD) manifold generated from high-fidelity numerical simulations. Unlike conventional reduced-order data assimilation methods that estimate independent snapshots or treat time as an additional parameter, RODAS reconstructs an entire dynamical trajectory in a single inference step while naturally incorporating parametric variability. We assess the proposed methodology on vortex shedding behind a circular cylinder for both Newtonian and non-Newtonian (Carreau-Yasuda) fluids. Numerical experiments demonstrate accurate reconstruction of high-resolution velocity fields from localized, low-resolution measurements, achieving sub-percent reconstruction errors with sufficiently rich reduced bases, robust performance under severe temporal undersampling, and accurate prediction of engineering quantities of interest such as the drag coefficient. These results demonstrate that RODAS provides an efficient framework for real-time, physics-informed reconstruction of unsteady flows from sparse experimental data.

发表机构

• School of Civil Engineering, Pontificia Universidad Católica de Valparaíso（天主教瓦帕拉索大学土木工程学院）
• Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile（智利圣地亚哥大学机械工程系）
• Computational Heat and Fluid Flow Lab, Universidad de Santiago de Chile（智利圣地亚哥大学计算热流体实验室）
• Department of Mechanical and Metallurgical Engineering, Pontificia Universidad Católica de Chile（智利天主教大学机械与冶金工程系）
• Department of Hydraulic and Environmental Engineering, Pontificia Universidad Católica de Chile（智利天主教大学水利与环境工程系）

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