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Data assimilation method to de-noise and de-filter particle image velocimetry data

Published online by Cambridge University Press:  19 August 2019

Jurriaan J. J. Gillissen Open the ORCID record for Jurriaan J. J. Gillissen [Opens in a new window] ,
Roland Bouffanais Open the ORCID record for Roland Bouffanais [Opens in a new window]  and
Dick K. P. Yue Open the ORCID record for Dick K. P. Yue [Opens in a new window]
Jurriaan J. J. Gillissen*
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Roland Bouffanais
Affiliation:
Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore
Dick K. P. Yue
Affiliation:
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: jurriaangillissen@gmail.com
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Abstract

We present a variational data assimilation method in order to improve the accuracy of velocity fields $\tilde{\boldsymbol{v}}$, that are measured using particle image velocimetry (PIV). The method minimises the space–time integral of the difference between the reconstruction $\boldsymbol{u}$ and $\tilde{\boldsymbol{v}}$, under the constraint, that $\boldsymbol{u}$ satisfies conservation of mass and momentum. We apply the method to synthetic velocimetry data, in a two-dimensional turbulent flow, where realistic PIV noise is generated by computationally mimicking the PIV measurement process. The method performs optimally when the assimilation integration time is of the order of the flow correlation time. We interpret these results by comparing them to one-dimensional diffusion and advection problems, for which we derive analytical expressions for the reconstruction error.

JFM classification

Mathematical Foundations: Computational methods Mathematical Foundations: Variational methods Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 196 - 213
Copyright
© 2019 Cambridge University Press 

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