Dynamics-Informed Data Assimilation in a Point-Vortex Model

Fast and accurate numerical models are critical for the tracking, prediction, and control of fluid flows. Traditional grid-based modelling techniques, though highly accurate, are often too slow for these purposes. So-called reduced-order models—which track abstract flow structures, rather than the details of fluid velocities at every point—are much faster, but the inherent coarseness of their modeling approximation makes them inaccurate. However, correcting a reduced-order model with observations of the fluid, a process known as data assimilation, could produce a model that has both the speed and accuracy required for real-time applications. We explore this hypothesis using the point-vortex model, which tracks only the vortices in the flow. Our primary goal in this exploration is to develop an intelligent assimilation strategy that can correct the solver’s mistakes with minimal computational effort. To achieve this, we employ knowledge about the system dynamics to determine when the corrections will be most effective and when they are not required. We call this new data assimilation strategy “Dynamics-Informed Assimilation”. We have performed several numerical experiments that demonstrate the success of this strategy in reducing the computational burden of gathering and processing the observations. These numerical experiments are a useful first step, but a real fluid flow is needed to ensure that our approach is practical for real-world applications. To this end, we plan to test our assimilation strategy with experimental data from a planar air jet in our laboratory. This is a break from traditional data assimilation research, in which numerical experiments are the norm. Exploring data assimilation in a controlled laboratory context will provide unique insight into the dynamics of the data assimilation process, and the knowledge gained will be of general interest to the data assimilation community. In the remainder of this section, we introduce the concepts that are central to our research—numerical modelling of fluid flows and data assimilation—and provide an overview of our dynamics-informed strategy and laboratory testbed.