State estimation in turbulent channel flow from limited observations

Wang, Mengze; Zaki, Tamer A.

doi:10.1017/jfm.2021.268

Cited by 32 publications

(18 citation statements)

References 60 publications

(131 reference statements)

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“…Results for observations of only one component of the stress or pressure at one time instance are the focus of this work, and will be discussed in detail in §§ 3.1 and 3.2. In order to place that discussion in context, however, we start by examining the capacity for state estimation when all three components are available as a function of time during the assimilation window; this preliminary step is a summary of a recent detailed study by Wang & Zaki (2021). The cost function for the collective observations over the entire time horizon is defined as where is the integral of the instantaneous cost function (2.2) over the observation window, and similarly for and .…”

Section: Methodsmentioning

confidence: 99%

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What is observable from wall data in turbulent channel flow?

Wang

Zaki

2022

J. Fluid Mech.

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Estimation of the initial state of turbulent channel flow from spatially and temporally resolved wall data is performed using adjoint-variational data assimilation. The estimated flow fields satisfy the Navier–Stokes equations and minimize a cost function defined as the difference between model predictions and the available observations. The accuracy of the predicted flow deteriorates with distance from the wall, most precipitously across the buffer layer beyond which only large-scale structures are reconstructed. To explain this trend, we examine the domain of dependence of the observations and the Hessian matrix of the state-estimation cost function, both of which are efficiently evaluated using adjoint fields initiated from impulses at wall sensors. Eigenanalysis of the Hessian is performed, and the eigenvalues are related to the capacity to reconstruct flow structures represented by the eigenvectors. Most of the eigenmodes decay beyond the buffer layer, thus demonstrating weak sensitivity of wall observations to the turbulence in the bulk. However, when the measurement time $t_m^{+} \gtrsim 20$ , some streamwise-elongated Hessian eigenfunctions remain finite in the outer flow, and correspond to the sensitivity of wall observations to outer large-scale motions. At much longer observation times, the adjoint field becomes chaotic as it amplifies exponentially, which is indicative of extreme gradients of the cost function and an ill-conditioned Hessian matrix, and both exacerbate the difficulty of estimating turbulence from wall observations.

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Section: Methodsmentioning

confidence: 99%

“…The estimation was accurate near the wall, but was nearly uncorrelated with the true initial flow state in the channel centre. As the Reynolds number is increased, the outer large-scale structures can also be reconstructed from wall observations using 4DVar (Wang & Zaki 2021).…”

Section: Introductionmentioning

confidence: 99%

What is observable from wall data in turbulent channel flow?

Wang

Zaki

2022

J. Fluid Mech.

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“…On the other hand, some improvement is achieved in matching τ 12 , even if the discrepancies from the reference profile remain significant. The difficulties in satisfactorily correcting the LES predictions in this data assimilation experiment may be quantified thanks to the linearized cost function J in (18). Since J is quadratic, its gradient with respect to the control vector w, which arises from the ensemble representation of the original control vector γ in (12), is straightforward to compute.…”

Section: Iii3 Ensemble Generation and Data Assimilation Parametersmentioning

confidence: 99%

“…Generally speaking, data assimilation enables the merging of experimental and numerical approaches and to overcome their inherent limitations, namely the scarcity of experimental data and the uncertainties in modeling and in the inputs of simulations [11]. Incidentally, as an alternative to DNS [12][13][14][15][16][17][18], recent studies have explored the possibilities of relying on LES for flow reconstruction/state estimation through data assimilation [19][20][21][22]. However, contrary to RANS where a number of studies exploited data assimilation to adjust turbulence models [23][24][25][26][27][28][29], the potential of data assimilation to enhance LES modeling has not been investigated to a similar extent, with very few exceptions [20,30].…”

Section: Introductionmentioning

confidence: 99%

“…the quantities being optimized, it generally requires significant resources to implement and to use. This is particularly true for unsteady problems, because the storage of the forward flow solution is required for the backward-in-time integration of the adjoint model over the whole considered time window [18,33]. The computational burden is thus very large for 3D flows, which is perhaps at the origin of the short time-window considered in [20] and of the restriction of the the assimilation to pairs of consecutive instants in [30].…”

Section: Introductionmentioning

confidence: 99%

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Ensemble-variational assimilation of statistical data in large eddy simulation

Mons¹,

Du²,

Zaki³

2021

Preprint

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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 fluctuations of the modeled subgrid tensor, and ultimately the first-and second-order flow statistics, two types of model corrections are considered. The first one optimizes the wall-normal profile of the Smagorinsky coefficient, while the second one introduces an adjustable steady forcing in the momentum equations to independently act on the mean flow. Using these two elements, the data assimilation procedure can satisfactorily modify the subgrid model and accurately recover reference flow statistics. The retrieved subgrid model significantly outperforms more elaborate baseline models such as dynamic and mixed models, in a posteriori testing. The robustness of the present data assimilation methodology is assessed by changing the Reynolds number and considering grid resolutions that are away from usual recommendations. Taking advantage of the stochastic formulation of EnVar, the developed framework also provides the uncertainty of the retrieved model.

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