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Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation [article]

Adam Larios, Elizabeth Carlson
2020 arXiv   pre-print
Moreover, we do so by showing a sequence of difference quotients converges to the unique solution of the sensitivity equations for both the 2D Navier-Stokes equations and the related data assimilation  ...  We rigorously prove the well-posedness of the formal sensitivity equations with respect to the Reynolds number corresponding to the 2D incompressible Navier-Stokes equations.  ...  Acknowledgements E.C. would like to give thanks for the kind hospitality of the COSIM group at Los Alamos National Laboratory where some of this work was completed.  ... 
arXiv:2007.01860v1 fatcat:oke5iufq4rfplixsedcwbh7ib4

A data assimilation algorithm: the paradigm of the 3D Leray-alpha model of turbulence [article]

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
2017 arXiv   pre-print
This study serves as an addendum to our recent work on abridged continuous data assimilation for the 2D Navier-Stokes equations.  ...  for recovering, through our data assimilation algorithm, the full solution; viz. the three components of velocity vector field and the temperature.  ...  Acknowledgements We would like to thank Professor M. Ghil for the stimulating exchange concerning the Charney conjecture and for pointing out to us some of the relevant references.  ... 
arXiv:1702.01506v1 fatcat:pnyzveembbe7hfwqlzey2jfxhu

Accuracy and stability of the continuous-time 3DVAR filter for the Navier–Stokes equation

D Blömker, K Law, A M Stuart, K C Zygalakis
2013 Nonlinearity  
This leads to a stochastic partial differential equation (SPDE) for state estimation, in the form of a damped-driven Navier-Stokes equation, with mean-reversion to the signal, and spatially-correlated  ...  This motivates study of the problem of accuracy and stability of 3DVAR filters for the Navier-Stokes equation. We work in the limit of high frequency observations and derive continuous time filters.  ...  Dirk Blömker would like to thank the center for its financial support.  ... 
doi:10.1088/0951-7715/26/8/2193 fatcat:4oersbzg4zc4hjzvm4qik5itui

Bayesian inverse problems for functions and applications to fluid mechanics

S L Cotter, M Dashti, J C Robinson, A M Stuart
2009 Inverse Problems  
In order to undertake a clean mathematical analysis we consider the two-dimensional Navier-Stokes equation on a torus.  ...  The detailed derivation of many estimates valid for the two-dimensional Navier-Stokes equation form a key component of the analysis here, and are collected together at the end of the paper.  ...  AMS is grateful to EPSRC and ONR for financial support; MD and SLC are grateful to the Warwick Postgraduate Fellowship fund and to EPSRC (respectively) for support of their graduate studies.  ... 
doi:10.1088/0266-5611/25/11/115008 fatcat:x2eqyfr4ubdznilwv7hwu3tlz4

Data assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
2016 Journal of Mathematical Analysis and Applications  
In this paper we propose a continuous data assimilation (downscaling) algorithm for the Bénard convection in porous media using only discrete spatial-mesh measurements of the temperature.  ...  at an exponential rate, asymptotically in time, to the unique exact unknown reference solution of the original system, associated with the observed (finite dimensional projection of) temperature data.  ...  Inspired by the recent algorithms proposed in [4, 15] , we introduced an abridged dynamic continuous data assimilation for the 2D Navier-Stokes equations (NSE) in [16] .  ... 
doi:10.1016/j.jmaa.2016.01.072 fatcat:djabwpgzxrblte6amu556sxtue

Data Assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements [article]

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
2015 arXiv   pre-print
In this paper we propose a continuous data assimilation (downscaling) algorithm for the B\'enard convection in porous media using only coarse mesh measurements of the temperature.  ...  at an exponential rate, asymptotically in time, to the unique exact unknown reference solution of the original system, associated with the observed (finite dimensional projection of) temperature data.  ...  Inspired by the recent algorithms proposed in [4, 15] , we introduced an abridged dynamic continuous data assimilation for the 2D Navier-Stokes equations (NSE) in [16] .  ... 
arXiv:1506.08678v2 fatcat:dp3ytard4fg7rnam3egs35i6ri

Applications of variational data assimilation in computational hemodynamics [chapter]

Marta D'Elia, Lucia Mirabella, Tiziano Passerini, Mauro Perego, Marina Piccinelli, Christian Vergara, Alessandro Veneziani
2012 Modeling, Simulation and Applications  
These data can be in fact merged with the numerical simulations for improving the accuracy and reliability of the computational tools.  ...  Several modeling and methodological problems related to this strategy are open, such as the analysis of the impact of the noise affecting the data, and the design of effective numerical solvers.  ...  Variational Assimilation of Velocity Data for the Incompressible Navier-Stokes Equations Bicuspid aortic valve (BAV) is the most common congenital heart defect, occurring in about 1% of the population  ... 
doi:10.1007/978-88-470-1935-5_12 fatcat:agzqszbwl5dfpdbwjztfk4q5jy

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  ...  (PID) framework as an enabler to account for localized modal deformation, which is a key element in accurate reduced order modeling of convective flows.  ...  Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness  ... 
arXiv:1910.07649v1 fatcat:7jlfk5nk4baglafsjkaagyzxfu

Uncovering near-wall blood flow from sparse data with physics-informed neural networks [article]

Amirhossein Arzani, Jian-Xun Wang, Roshan M. D'Souza
2021 arXiv   pre-print
By leveraging knowledge about the governing equations (herein, Navier-Stokes), PINN overcomes the large data requirement in deep learning.  ...  Physics-informed neural networks (PINN) provide a flexible deep learning framework to integrate mathematical equations governing blood flow with measurement data.  ...  Data Availability The Pytorch codes and data used to generate the results in the manuscript are available on Github https://github.com/amir-cardiolab/PINN-wss.  ... 
arXiv:2104.08249v2 fatcat:ylaaiirnbrfjdp74bxrxvpgxty

Continuous Data Assimilation For the 3D Ladyzhenskaya Model: Analysis and Computations [article]

Yu Cao, Andrea Giorgini, Michael Jolly, Ali Pakzad
2021 arXiv   pre-print
We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations.  ...  The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with the observed, spatially coarse data.  ...  The model corresponding to p = 2 reduces to the Navier-Stokes equations (NSE) with kinematic viscosity equal to (ν 0 + ν 1 ).  ... 
arXiv:2108.03513v1 fatcat:sytbtofrwvbi5alc7dnvy5iwsq

Downscaling the 2D Bénard convection equations using continuous data assimilation

M. U. Altaf, E. S. Titi, T. Gebrael, O. M. Knio, L. Zhao, M. F. McCabe, I. Hoteit
2017 Computational Geosciences  
We consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Benard convection equations into a finer grid.  ...  SUMMARY We consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Bénard convection equations into a finer grid.  ...  The Bénard convection equations solve the reduced form of Navier-Stokes equations and are one of the classical problems in the heat transfer literature [29] .  ... 
doi:10.1007/s10596-017-9619-2 fatcat:74v6bmsyxnfxhiy767gkp7hzwa

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  
), due to its potential for broad and practical utility.  ...  We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV  ...  They thank Gillian Murphy for secretarial assistance in preparation of the paper.  ... 
doi:10.1155/2013/395081 pmid:23690874 pmcid:PMC3652115 fatcat:hihr7kfuframtitblrxb2g27mm

Downscaling the 2D Benard Convection Equations Using Continuous Data Assimilation [article]

M. U. Altaf, E. S. Titi, O. M. Knio, L. Zhao, M. F. McCabe, I. Hoteit
2015 arXiv   pre-print
We consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Benard convection equations into a finer grid.  ...  The main contribution of this study is a performance analysis of CDA for downscaling measurements of temperature and velocity.  ...  The Bénard convection equations solve the reduced form of Navier-Stokes equations and are one of the classical problems in the heat transfer literature [29] .  ... 
arXiv:1512.04671v2 fatcat:o6nox5tkc5h4fo2csuxijgzieq

Approximation of Bayesian Inverse Problems for PDEs [article]

S.L. Cotter, M. Dashti, A.M. Stuart
2009 arXiv   pre-print
of the initial condition for the Stokes or Navier-Stokes equation from Lagrangian and Eulerian observations respectively.  ...  The ideas are illustrated with the classical inverse problem for the heat equation, and then applied to some more complicated non-Gaussian inverse problems arising in data assimilation, involving determination  ...  Acknoweldgements The authors are grateful to the EPSRC, ERC and ONR for financial support.  ... 
arXiv:0909.2126v1 fatcat:cdrsvomvdfgyvc6g3lzevlg2xm

The independent set perturbation adjoint method: A new method of differentiating mesh-based fluids models

F. Fang, C. C. Pain, I. M. Navon, G. J. Gorman, M. D. Piggott, P. A. Allison
2010 International Journal for Numerical Methods in Fluids  
GOVERNING EQUATIONS Two systems of partial differential equations used to illustrate the application of the method are the Burgers' equation and the Navier-Stokes equations.  ...  The method is applied to two problems: the Burgers' equation and the Navier-Stokes equations applied to ocean gyre circulation in Section 7 followed by discussion. Finally, conclusions are drawn.  ...  Many thanks to Tamzin Mole for helping in the technical write up of this work and to Joe Fang for providing the artwork.  ... 
doi:10.1002/fld.2297 fatcat:r5nmjmw5kjfehiwhb6o6m73pay
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