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Flow state estimation in the presence of discretization errors

Published online by Cambridge University Press:  11 March 2020

Andre F. C. da Silva Open the ORCID record for Andre F. C. da Silva [Opens in a new window]  and
Tim Colonius Open the ORCID record for Tim Colonius [Opens in a new window]
Andre F. C. da Silva*
Affiliation:
Department of Civil and Mechanical Engineering, California Institute of Technology, Pasadena, CA 91101, USA
Tim Colonius
Affiliation:
Department of Civil and Mechanical Engineering, California Institute of Technology, Pasadena, CA 91101, USA
*
†Email address for correspondence: andre.fernando.t10@gmail.com
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Abstract

Ensemble data assimilation methods integrate measurement data and computational flow models to estimate the state of fluid systems in a robust, scalable way. However, discretization errors in the dynamical and observation models lead to biased forecasts and poor estimator performance. We propose a low-rank representation for this bias, whose dynamics is modelled by data-informed, time-correlated processes. State and bias parameters are simultaneously corrected online with the ensemble Kalman filter. The proposed methodology is then applied to the problem of estimating the state of a two-dimensional flow at modest Reynolds number using an ensemble of coarse-mesh simulations and pressure measurements at the surface of an immersed body in a synthetic experiment framework. Using an ensemble size of 60, the bias-aware estimator is demonstrated to achieve at least 70 % error reduction when compared to its bias-blind counterpart. Strategies to determine the bias statistics and their impact on the estimator performance are discussed.

JFM classification

Flow Control: Control theory Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A10
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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