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"note": "cite arxiv:2109.12295","abstract": "A non-intrusive data assimilation methodology is developed to improve the\r\nstatistical predictions of large-eddy simulations (LES). The\r\nensemble-variational (EnVar) approach aims to minimize a cost function that is\r\ndefined as the discrepancy between LES predictions and reference statistics\r\nfrom experiments or, in the present demonstration, independent direct numerical\r\nsimulations (DNS). This methodology is applied to adjust the Smagorinsky\r\nsubgrid model and obtain data assimilated LES (DA-LES) which accurately\r\nestimate the statistics of turbulent channel flow. To separately control the\r\nmean and fluctuations of the modeled subgrid tensor, and ultimately the first-\r\nand second-order flow statistics, two types of model corrections are\r\nconsidered. The first one optimizes the wall-normal profile of the Smagorinsky\r\ncoefficient, while the second one introduces an adjustable steady forcing in\r\nthe momentum equations to independently act on the mean flow. Using these two\r\nelements, the data assimilation procedure can satisfactorily modify the subgrid\r\nmodel and accurately recover reference flow statistics. The retrieved subgrid\r\nmodel significantly outperforms more elaborate baseline models such as dynamic\r\nand mixed models, in a posteriori testing. The robustness of the present data\r\nassimilation methodology is assessed by changing the Reynolds number and\r\nconsidering grid resolutions that are away from usual recommendations. Taking\r\nadvantage of the stochastic formulation of EnVar, the developed framework also\r\nprovides the uncertainty of the retrieved model.",
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"label" : "Wave equation model for solving advection-diffusion equation",
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"volume": "37","number": "16","pages": "2717-2733","abstract": "This paper presents a Wave Equation Model (WEM) to solve advection dominant Advection\u2013Diffusion (A\u2013D) equation. It is known that the operator-splitting approach is one of the effective methods to solve A\u2013D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first-order advection equation, the present wave equation model solves a second-order equivalent wave equation whose solution is identical to that of the first-order advection equation. Numerical examples of 1-D and 2-D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1-D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.",
"doi" : "10.1002/nme.1620371603",
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"label" : "Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods",
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"pub-type": "article",
"journal": "Complexity",
"year": "2018",
"url": "https://www.hindawi.com/journals/complexity/2018/6920783/",
"author": [
"Soledad Le Clainche","José M. Vega"
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{"first" : "Soledad", "last" : "Le Clainche"},
{"first" : "José M.", "last" : "Vega"}
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"volume": "2018","number": "6920783","abstract": "This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purely data-driven, using either numerical or experimental data, and permit reconstructing the given data and identifying the temporal growth rates and frequencies involved in the dynamics and the spatial growth rates and wavenumbers in the case of the spatiotemporal Koopman decomposition. Thus, they may be used to either identify and extrapolate the dynamics from transient behavior to permanent dynamics or construct efficient, purely data-driven reduced order models.\"/>