Study of the energy convergence of the Karhunen-Loeve decomposition applied to the large-eddy simulation of a high-Reynolds-number pressure-driven boundary layer

用于随机场的双保真Karhunen-Loève展开代理模型及其主动学习

Bifidelity Karhunen-Loève Expansion Surrogate with Active Learning for Random Fields

本文提出双保真Karhunen-Loève展开代理模型BF-KLE-AL，结合低保真与高保真模拟，并通过基于高斯过程回归的主动学习策略自适应选择高保真样本，在多个算例中显著提升随机场预测精度与样本效率。

Gaussian process regression and conditional Karhunen-Loéve models for data assimilation in inverse problems

We present a model inversion algorithm, CKLEMAP, for data assimilation and parameter estimation in partial differential equation models of physical systems with spatially heterogeneous parameter fields. These fields are approximated using low-dimensional conditional Karhunen-Loéve expansions, which are constructed using Gaussian process regression models of these fields trained on the parameters' measurements. We then assimilate measurements of the state of the system and compute the maximum a posteriori estimate of the CKLE coefficients by solving a nonlinear least-squares problem. When solvi…

Dynamics of propagating turbulent pipe flow structures. Part I: Effect of drag reduction by spanwise wall oscillation

The results of a comparative analysis based upon a Karhunen-Loève expansion of turbulent pipe flow and drag reduced turbulent pipe flow by spanwise wall oscillation are presented. The turbulent flow is generated by a direct numerical simulation at a Reynolds number $Re_τ= 150$. The spanwise wall oscillation is imposed as a velocity boundary condition with an amplitude of $A^+ = 20$ and a period of $T^+ = 50$. The wall oscillation results in a 27% mean velocity increase when the flow is driven by a constant pressure gradient. The peaks of the Reynolds stress and root-mean-squared velocities shi…

The consequences of finite-time proper orthogonal decomposition for an extensively chaotic flow field

The use of proper orthogonal decomposition (POD) to explore the complex fluid flows that are common in engineering applications is increasing and has yielded new physical insights. However, for most engineering systems the dimension of the dynamics is expected to be very large yet the flow field data is available only for a finite time. In this context, it is important to establish the convergence of the POD in order to accurately estimate such quantities as the Karhunen-Loève dimension. Using direct numerical simulations of Rayleigh-Bénard convection in a finite cylindrical geometry we explor…

Reconstruction of turbulent flow fields from lidar measurements based on large-eddy simulation

We investigate the reconstruction of a turbulent flow field in the atmospheric boundary layer from a time series of lidar measurements, using Large-Eddy Simulations (LES) and a 4D-Var data assimilation algorithm. This leads to an optimisation problem in which the error between measurements and simulations is minimised over an observation time horizon. To exploit the spatial coherence of the turbulence, we use a quadratic regularisation in the objective function, that is based on the two-point covariance matrix. Moreover, to improve conditioning, and remove continuity constraints, the problem i…