N. Ross, E. Bradley, and J. Hertzberg, "Dynamics-Informed Data Assimilation in a Qualitative Fluids Model," International Workshop on Qualitative Reasoning, 2006


Fast and accurate numerical models are critical for the modelling, prediction, and control of fluid flows. Direct numerical simulation (DNS) methods, though accurate, are often too slow for these purposes. So-called reduced-order models are faster because they use fewer state variables to approximate the flow physics. Different tactics are used for this dimensional reduction. Some approaches simply coarsen the numerical grain of the approximation. Others take a more-qualitative approach, decomposing the flow into abstract features---coherent structures like vortices, for instance---and modelling the dynamics of those features. Regardless of the tactics involved, the inherent approximations make reduced-order models inaccurate. The premise of this paper is that periodically correcting such a model with observations of the fluid---a process known as data assimilation---can produce a "data-adaptive" model that is both fast and accurate. This idea has been explored in depth by the numerical weather prediction community in the context of DNS models. The goal of this paper is to explore data assimilation in the context of a model that treats a fluid flow as a collection of vortices. There are two challenges in assimilating data into such a model: correction dynamics and computational cost. The strategy described here solves both of those problems using knowledge about the flow dynamics to intelligently select when and where to apply the correction.

Full paper here.