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Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations [article]

Matthew Gardner, Adam Larios, Leo G. Rebholz, Duygu Vargun, Camille Zerfas
2020 arXiv   pre-print
We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied  ...  These properties hold if nudging is applied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time.  ...  We consider in this paper discretizations of a continuous data assimilation (CDA) enhancement applied to the following velocity-vorticity (VV) formulation of the 2D NSE: u t − ν∆u + ω × u + ∇P = f, ∇ ·  ... 
arXiv:2006.07295v1 fatcat:c54efutzijhptjqmci3uhj25ny

Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations

Matthew Gardner, School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, 29634, USA, Adam Larios, Leo G. Rebholz, Duygu Vargun, Camille Zerfas, Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA
2020 Electronic Research Archive  
We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied  ...  These properties hold if nudging is applied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time.  ...  We consider in this paper discretizations of a continuous data assimilation (CDA) enhancement applied to the following velocity-vorticity (VV) formulation of the 2D NSE: u t − ν∆u + ω × u + ∇P = f, ∇ ·  ... 
doi:10.3934/era.2020113 fatcat:buma2lq6j5ehvjfdtlberjhrui

Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study

Aseel Farhat, Hans Johnston, Michael Jolly, Edriss S. Titi
2018 Journal of Scientific Computing  
We introduce a continuous (downscaling) data assimilation algorithm for the 2D Bénard convection problem using vorticity or local circulation measurements only.  ...  In this algorithm, a nudging term is added to the vorticity equation to constrain the model.  ...  Acknowledgements This work was initiated while the authors were visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the National Science  ... 
doi:10.1007/s10915-018-0686-x fatcat:kvsd4co7hvcwfpyiqdcbq7ehly

Assimilation of nearly turbulent Rayleigh-Bénard flow through vorticity or local circulation measurements: a computational study [article]

Aseel Farhat, Hans Johnston, Michael S. Jolly, Edriss S. Titi
2017 arXiv   pre-print
We introduce a continuous (downscaling) data assimilation algorithm for the 2D B\'enard convection problem using vorticity or local circulation measurements only.  ...  In this algorithm, a nudging term is added to the vorticity equation to constrain the model.  ...  Acknowledgements This work was initiated while the authors were visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the National Science  ... 
arXiv:1709.02417v1 fatcat:gpneqaa5bnfpfhe57cf5bbpvge

Divergence-Free Motion Estimation [chapter]

Isabelle Herlin, Dominique Béréziat, Nicolas Mercier, Sergiy Zhuk
2012 Lecture Notes in Computer Science  
A 4DVAR-like image assimilation method is used to generate an estimate of the vorticity field given image observations.  ...  The method is then applied to ocean satellite data to demonstrate its performance on the real images.  ...  The vorticity dynamics is described by a 2D approximation of the Navier-Stokes equations, that requires the simultaneous knowledge of velocity and vorticity.  ... 
doi:10.1007/978-3-642-33765-9_2 fatcat:k4g3yln5n5a57jsmmqge76mine

Exponentially convergent data assimilation algorithm for Navier-Stokes equations

Sergiy Zhuk, Tigran T. Tchrakian, Jason Frank
2017 2017 American Control Conference (ACC)  
The paper presents a new state estimation algorithm for a bilinear equation representing the Fourier- Galerkin (FG) approximation of the Navier-Stokes (NS) equations on a torus in R2.  ...  To demonstrate the results we apply the proposed algorithm to the reconstruction a chaotic fluid flow from incomplete and noisy data.  ...  In this paper we design an exponentially convergent state estimator for a so called vorticity equation, the vorticity-streamfunction formulation of the Navier-Stokes (NS) equations in two spatial dimensions  ... 
doi:10.23919/acc.2017.7963448 dblp:conf/amcc/ZhukTF17 fatcat:lf3s2o4v7bbypnt6lrcdtyyiw4

A Modular Collaborative Parallel CFD Workbench [chapter]

Kwai L. Wong, A. Jerry Baker
2001 Lecture Notes in Computer Science  
This paper introduces the concept and details the development of a user-adapted computational simulation software platform prototype on the Internet.  ...  A key element of this will involve development of computational software enabling utilization of all HPCC advances.  ...  Acknowledgments The authors would like to acknowledge the support of computer resources from the Computer Science and Mathematics Division and the Solid State Division at Oak Ridge National Laboratory.  ... 
doi:10.1007/3-540-45545-0_42 fatcat:addzcx4eqfftpmhupwlgei5sjq

Memory embedded non-intrusive reduced order modeling of non-ergodic flows [article]

Shady E. Ahmed, Sk. Mashfiqur Rahman, Omer San, Adil Rasheed, Ionel M. Navon
2019 arXiv   pre-print
Our applications for convection dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than  ...  the POD-Galerkin method, and could be a key enabler towards near real-time predictions of unsteady flows.  ...  The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.  ... 
arXiv:1910.07649v1 fatcat:7jlfk5nk4baglafsjkaagyzxfu

Robust Processing of Optical Flow of Fluids

A Doshi, A G Bors
2010 IEEE Transactions on Image Processing  
The proposed methodology, which relies on Navier-Stokes equations, is used for processing fluid optical flow by using a succession of processing stages such as advection, diffusion and mass conservation  ...  A new approach is developed for detecting fluid flow structures such as vortices. The proposed methodology is applied on artificially generated vector fields as well as on various image sequences.  ...  The synthetic flow is created using the vorticity-stream formulation of the Navier-Stokes equations [8] .  ... 
doi:10.1109/tip.2010.2048614 pmid:20409993 fatcat:clvv6ia6yzdodkdxc7ha43z2hm

Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation

A. Gronskis, D. Heitz, E. Mémin
2013 Journal of Computational Physics  
This method allows to denoise experimental velocity fields and to reconstruct a continuous trajectory of motion fields from discrete and unstable measurements.  ...  The proposed method is based on variational data assimilation and adjoint-based optimization.  ...  Continuous Model The dynamical model that relates the state function to the unknown of our inverse problem is based on pressurevelocity formulation of Navier-Stokes equations and is briefly described below  ... 
doi:10.1016/j.jcp.2013.01.051 fatcat:dlryufo2dvfntnxpwzwo4j26wa

The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations [article]

Trenton Franz, Adam Larios, Collin Victor
2021 arXiv   pre-print
We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations.  ...  We end with a discussion of possible applications to real-world data collection strategies that may lead to substantial improvements in predictive capabilities.  ...  Acknowledgments Author T.E.F. acknowledges the financial support of the USDA National Institute of Food and Agriculture Hatch project #1020768 and project #2019-67021-29312.  ... 
arXiv:2110.10362v1 fatcat:nw7i4qvhxnfe5lvjyv3wp4o3ve

Bayesian inference for data assimilation using Least-Squares Finite Element methods

Richard P Dwight
2010 IOP Conference Series: Materials Science and Engineering  
The technique is applied to incompressible Navier-Stokes flow in a pipe with added velocity data, where its effectiveness, robustness to noise, and application to inverse problems is demonstrated.  ...  case of incompressible Navier-Stokes flow [1] .  ...  Section 4 completes the presentation with numerical examples of the method applied to Navier-Stokes flow with added velocity data.  ... 
doi:10.1088/1757-899x/10/1/012224 fatcat:nb5b5oikarbopjaenjszg4gxfq

Left Ventricular Flow Analysis: Recent Advances in Numerical Methods and Applications in Cardiac Ultrasound

Iman Borazjani, John Westerdale, Eileen M. McMahon, Prathish K. Rajaraman, Jeffrey J. Heys, Marek Belohlavek
2013 Computational and Mathematical Methods in Medicine  
The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics.  ...  The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation.  ...  They thank Gillian Murphy for secretarial assistance in preparation of the paper.  ... 
doi:10.1155/2013/395081 pmid:23690874 pmcid:PMC3652115 fatcat:hihr7kfuframtitblrxb2g27mm

Skin friction and pressure: the "footprints" of turbulence

Thomas R. Bewley, Bartosz Protas
2004 Physica D : Non-linear phenomena  
Combining this fact with the analyticity of solutions of the Navier-Stokes equation on the attractor, in theory complete reconstruction of a turbulent flow in a channel at time t is possible given only  ...  The idealized problem of a continuous distribution of both actuation and sensing on the wall is not quite physically realizable anyway; how this configuration might be approximated in a real implementation  ...  Acknowledgements This article is dedicated to the memory of Uwe Dallmann, whose characterizations of the "footprints" of separated flows (see, e.g., Theofilis, Hein, & Dallmann 2000) inspired the present  ... 
doi:10.1016/j.physd.2004.02.008 fatcat:b5f56fpakvednejgo36n4mvmwe

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

G. Artana, A. Cammilleri, J. Carlier, E. Mémin
2012 Journal of Computational Physics  
Both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a Galerkin projection of the Navier Stokes equation.  ...  In this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows.  ...  LES was performed for a time duration of ≃ 52 vortex shedding cycles to ensure a convergence of the 2nd order statistics.  ... 
doi:10.1016/j.jcp.2012.01.010 fatcat:5ekqsoizgfdqrpqv2tdmvgsz74
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