Flow state estimation in the presence of discretization errors

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.