This paper proposes a new data assimilation method for recovering high fidelity turbulent flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion (POD-Inversion) data assimilation method. Aiming at the flows including shock wave discontinuities or separated flows at high angle of attack, the proposed method can reconstruct high-fidelity turbulent flow field combining with experimental distributed force coefficients. We firstly perform the POD analysis to the turbulent eddy viscosity fields computed by SA model and obtain the base POD modes. Then optimized the POD coefficients by global optimization algorithm coupling with the Navier-Stokes equations solver. The high-fidelity turbulent flied are recovered by several main modes, which can dramatically reduce the dimensions of the system. The effectiveness of the method is verified by the cases of transonic flow around the RAE2822 airfoil at high Reynolds numbers and the separated flow at high angles of attack. The results demonstrate that the proposed assimilation method can recover the turbulent flow field which optimally match the experimental data, and significantly reduce the error of pressure coefficients. The proposed data assimilation method can offer high-fidelity field data for turbulent model based on machine learning.
In this article, we provide a methodology to reconstruct high-Reynolds number turbulent mean-flows from few time-averaged measurements. A turbulent flow over a backward-facing step at Re = 28275 is considered to illustrate the potential of the approach. The data-assimilation procedure, based on a variational approach, consists in correcting a given baseline model by tuning space-dependent source terms such that the corresponding solution matches available measurements (obtained here from direct-numerical simulations). The baseline model chosen here consists in Reynolds-Averaged-Navier-Stokes (…
Turbulent problems in industrial applications are predominantly solved using Reynolds Averaged Navier Stokes (RANS) turbulence models. The accuracy of the RANS models is limited due to closure assumptions that induce uncertainty into the RANS modeling. We propose the use of deep learning algorithms via convolution neural networks along with data from direct numerical simulations to extract the optimal set of features that explain the evolution of turbulent flow statistics. Statistical tests are used to determine the correlation of these features with the variation in the quantities of interest…
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of high-fidelity data and the convergence and stability problem in the coupling process of turbulence models and the RANS solvers. In this paper, we propose an improved ensemble kalman inversion method as a unified approach of data assimilation and turbulence modeling for separated flows at high Reynolds numbers. The trainable parameters of the DNN are optimize…
A non-intrusive data assimilation methodology is developed to improve the statistical predictions of large-eddy simulations (LES). The ensemble-variational (EnVar) approach aims to minimize a cost function that is defined as the discrepancy between LES predictions and reference statistics from experiments or, in the present demonstration, independent direct numerical simulations (DNS). This methodology is applied to adjust the Smagorinsky subgrid model and obtain data assimilated LES (DA-LES) which accurately estimate the statistics of turbulent channel flow. To separately control the mean and…
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data assimilation scheme is developed, which exploits closed analytic formulae for updating the unobserved state variables. Therefore, it is computationally efficient and accurate. The new data assimilation scheme is combined with a simple reduced order modeling technique that involves a cheap closure approximation and a noise inflation. In such a way, many complic…
Analyzing the validity and success of a data assimilation algorithm when some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm, a rigorous justification to an earlier conjecture of Charney which states that temperature histo…
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that significantly accelerates the computational efficiency of Lagrangian data assimilation. The algorithm starts with a Fourier transform of the high-dimensional flow field, which is followed by an effective model reduction that retains only a small subset of the Fourier coefficients corresponding to the energetic modes. Then a linear stochastic model is developed …
The potential for data-driven applications to scale-resolving simulations of turbulent flows is assessed herein. Multigrid sequential data assimilation algorithms have been used to calibrate solvers for Large Eddy Simulation for the analysis of the high-Reynolds-number flow around a rectangular cylinder of aspect ratio 5:1. This test case has been chosen because of a number of physical complexities which elude accurate representation using reduced-order numerical simulation. The results for the statistical moments of the velocity and pressure flow field show that the data-driven techniques emp…
Previous works have shown that the small-scale information of incompressible homogeneous isotropic turbulence (HIT) is fully recoverable as long as sufficient large-scale structures are continuously enforced through temporally continuous data assimilation (TCDA). In the current work, we show that the assimilation time step can be relaxed to values about 1 $\sim$ 2 orders larger than that for TCDA, using a temporally sparse data assimilation (TSDA) strategy, while the accuracy is still maintained or even slightly better in the presence of non-negligible large-scale errors. The one-step data ass…
We investigate the prediction of the turbulent flow around a canonical square cylinder at Re= 22000 solving the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The limitations of URANS modelling are overcome through the application of a data assimilation technique involving a feedback control term, allowing to drive the URANS predictions towards reference data. Using regularly-spaced temporally-resolved reference data that are extracted from DNS, we assess the abilities of the data assimilation methodology in improving the unsteady URANS predictions. While improving the low-frequen…
Mean flow data assimilation using physics-constrained Graph Neural Networks
Dipartimento di Meccanica, Matematica e Management Politecnico di Bari（巴里理工学院机械、数学与管理系）；LISN-CNRS Université Paris-Saclay（巴黎萨克雷大学LISN-CNRS）；Digital Sciences & Technologies Department SafranTech（SafranTech数字科学与技术部门）
本文提出将 RANS 伴随梯度作为物理约束嵌入 GNN 训练，并结合 FEM 处理非结构化 CFD 数据，以在稀疏、含噪或缺损条件下提升钝体平均流重建精度。
Data assimilation of flow MRI data into RANS models with algebraic closures
Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, UK（英国剑桥大学工程系）；Department of Bioengineering, Stanford University, Stanford, CA, USA（美国斯坦福大学生物工程系）；Department of Radiology, Stanford University, Stanford, CA, USA（美国斯坦福大学放射系）；Stanford Cardiovascular Institute, Stanford University, Stanford, CA, USA（美国斯坦福大学心血管研究所）
We apply the four dimensional variational method to reconstruct the small scales of three-dimensional turbulent velocity fields with a moderate Reynolds number, given a time sequence of measurement data on a coarse set of grid points. The results show that, reconstruction is successful when the resolution of the measurement data, given in terms of the wavenumber, is at the order of the threshold value $k_c = 0.2η_K^{-1}$ where $η_K$ is the Kolmogorov length scale of the flow. When the data are available over a period of one large eddy turn-over time scale, the filtered enstrophy and other smal…
Synchronization of turbulence in channel flow is investigated using continuous data assimilation. The flow is unknown within a region of the channel. Beyond this region the velocity field is provided, and is directly prescribed in the simulation, while the pressure is unknown throughout the entire domain. Synchronization takes place when the simulation recovers the full true state of the flow, or in other words when the missing region is accurately re-established, spontaneously. Successful synchronization depends on the orientation, location and size of the missing layer. For friction Reynolds…
The problem of an accurate Eulerian-Lagrangian modeling of inertial particle dispersion in Large Eddy Simulation (LES) of turbulent wall-bounded flows is addressed. We run Direct Numerical Simulation (DNS) for turbulent channel flow at shear Reynolds numbers equal to 150 and 300 and corresponding a-priori and a-posteriori LES on differently coarse grids. We then tracked swarms of different inertia particles and we examined the influence of filtering and of Sub-Grid Scale (SGS) modeling for the fluid phase on particle velocity and concentration statistics. We also focused on how particle prefer…
A previously developed modeling procedure for large eddy simulations (LESs) is extended to allow physical space implementations for inhomogeneous flows. The method is inspired by the well-established theoretical analyses and numerical investigations of homogeneous, isotropic turbulence. A general procedure that focuses on recovering the full subgrid scale (SGS) dissipation from resolved fields is formulated, combining the advantages of both the structural and the functional strategy of modeling. The interscale energy transfer is obtained from the test-filtered velocity field, corresponding sub…
We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved large-eddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall ($\sim$ 10 wall units), while still resolving the near-wall region, to present a new path to save the computational cost. Convolutional neural network (CNN) is utilized to estimate a virtual wall-surface velocity from $x-z$ sectional fields near the wall, whose training data are generated by a direct numerical simulation (DNS) at ${\rm Re}_τ=180$. The virtual wall…
This paper examines the mechanisms of coherent structure interactions in spatially evolving turbulent free shear layers at different values of the velocity ratio parameter λ=$(U_1-U_2)/(U_1+U_2)$, where $U_1$ and $U_2 (\leq U_1)$ are the free stream velocities on either side of the layer. The study employs the point-vortex (or vortex-gas) model presented in part I (arXiv:1509.00603) which predicts spreading rates that are in the close neighborhood of results from most high Reynolds number experiments and 3D simulations. The present (2D) simulations show that the well-known steep-growth merger …
Transferable inference of turbulence models for urban flows with the Parameter-Regularised Ensemble Kalman Filter
Université Libre de Bruxelles（布鲁塞尔自由大学）；Aero-Thermo-Mechanics Laboratory（气动热力学实验室）；Brussels Institute for Thermal-Fluid Systems and Clean Energy (BRITE)（布鲁塞尔热流体系统与清洁能源研究所）；Department of Aeronautics, Imperial College London（帝国理工学院航空系）；I-X, Imperial College London（帝国理工学院I-X）；DIMEAS, Politecnico di Torino（都灵理工大学）；Brussels Institute for Advanced Studies (BrIAS)（布鲁塞尔高等研究院）；WEL Research Institute（WEL研究所）
A Comprehensive Analysis of the Relation between Intermittency and Dissipation in Non-Homogeneous Turbulent Flows
Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI（格勒诺布尔阿尔卑斯大学）；Institut für Physik und ForWind, Universität Oldenburg（奥尔登堡大学）；Univ. Lille, CNRS, ONERA, Arts et Métiers ParisTech, Centrale Lille, FRE 2017 - LMFL - Laboratoire de Mécanique des fluides de Lille - Kampé de Feriet（里尔大学）；Institut universitaire de France (IUF)（法国高等研究院）
Resolving Turbulent Magnetohydrodynamics: A Hybrid Operator-Diffusion Framework
National Center for Supercomputing Applications, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校国家超级计算中心）；Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Data Science and Learning Division, Argonne National Laboratory（阿贡国家实验室数据科学与学习部门）；Department of Computer Science, The University of Chicago（芝加哥大学计算机科学系）；Department of Astronomy, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校天文学系）；Department of Physics and Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文学系）
