Thesis Defense - Ross

The standard grid-based approach to modelling fluid flows -- termed direct numerical simulation (DNS) -- achieves impressive accuracy for most flows. However, DNS simulations are very compute-intensive, so they are currently impractical for real-time application domains such as flow control. Several reduced-order modelling techniques are available that make various approximations to the Navier-Stokes equations governing fluid dynamics. The point-vortex method is one such technique that achieves a reduction in complexity by making simplifying assumptions about the vorticity distribution and representing the entire flow with a collection of point vortices. The resulting dynamics are governed by an ordinary differential equation, which simplifies the physics significantly. These simplifications are not without penalty -- point-vortex simulations are typically much less accurate than DNS schemes. However, if the point-vortex model could be corrected with observations of the physical system -- a process known as data assimilation -- the resulting simulation might be sufficiently accurate for modelling and control applications. Care must be taken to ensure that the computational costs of the data assimilation scheme do not destroy the speed advantages of the point-vortex model.

In this thesis, we evaluate point-vortex data assimilation to determine the most efficient and effective assimilation strategy. We have proposed several dynamics-informed approaches that attempt to use the system dynamics to determine when the model needs a correction. The goal is to avoid the computational cost of correction when the model is performing well. We compare our dynamics-informed techniques to the standard approach in which the model is corrected at periodic intervals. Numerical experiments with several different vortex configurations and assimilation algorithms facilitate this comparison. The dynamics-informed techniques work very well for some vortex configurations, with a significant decrease in computational cost as compared to periodic correction. For other configurations, we identified some patterns in the vortex dynamics that can degrade the performance of dynamics-informed techniques. To ensure that our results apply to real-world flows, we have also performed a thorough analysis of assimilation using data from a laboratory planar air jet.