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ISSN 打印: 2152-5080

ISSN 在线: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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DATA ASSIMILATION FOR NAVIER-STOKES USING THE LEAST-SQUARES FINITE-ELEMENT METHOD

卷 8, 册 5, 2018, pp. 383-403
DOI: 10.1615/Int.J.UncertaintyQuantification.2018021021
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摘要

We investigate theoretically and numerically the use of the least-squares finite-element method (LSFEM) to approach data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is based on a stress-velocity-pressure (S-V-P) first-order formulation, using discrete counterparts of the Sobolev spaces H(div)×H1×L2 for the variables respectively. In general, S-V-P formulations are promising when the stresses are of special interest, e.g., for non-Newtonian, multiphase or turbulent flows. Resolution of the system is via minimization of a least-squares functional representing the magnitude of the residual of the equations. A simple and immediate approach to extend this solver to data assimilation is to add a data-discrepancy term to the functional. Whereas most data assimilation techniques require a large number of evaluations of the forward simulation and are therefore very expensive, the approach proposed in this work uniquely has the same cost as a single forward run. However, the question arises: what is the statistical model implied by this choice? We answer this within the Bayesian framework, establishing the latent background covariance model and the likelihood. Further we demonstrate that−in the linear case−the method is equivalent to application of the Kalman filter, and derive the posterior covariance. We practically demonstrate the capabilities of our method on a backward-facing step case. Our LSFEM formulation (without data) is shown to have good approximation quality, even on relatively coarse meshes−in particular with respect to mass conservation and reattachment location. Adding limited velocity measurements from experiment, we show that the method is able to correct for discretization error on very coarse meshes, as well as correct for the influence of unknown and uncertain boundary conditions.

对本文的引用
  1. Salman S., Talib A.R. Abu, Saadon S., Sultan M.T. Hameed, Hybrid nanofluid flow and heat transfer over backward and forward steps: A review, Powder Technology, 363, 2020. Crossref

  2. Clark Ed, Katzourakis Nikos, Muha Boris, Vectorial variational problems in L ∞ constrained by the Navier–Stokes equations* , Nonlinearity, 35, 1, 2022. Crossref

  3. Averweg Solveigh, Schwarz Alexander, Schwarz Carina, Schröder Jörg, Least‐squares formulation to solve non‐Newtonian fluid flow and application of data assimilation in 2D, PAMM, 21, 1, 2021. Crossref

  4. Schwarz Carina, Schröder Jörg, Simulating sea ice drift in the Southern Ocean incorporating real wind data using the LSFEM, PAMM, 21, 1, 2021. Crossref

  5. Averweg Solveigh, Schwarz Alexander, Schwarz Carina, Schröder Jörg, 3D modeling of generalized Newtonian fluid flow with data assimilation using the least-squares finite element method, Computer Methods in Applied Mechanics and Engineering, 392, 2022. Crossref

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