Research

As a member of NASA's Space Launch System (SLS) aerosciences task team, I and my collaborators work to develop new analytical tools which will modernize our national space infrastructure. Our work in data fusion yields new methods through which we can reconcile the myriad simulations and experiments of the largest rocket ever designed. Our work in reduced-order modeling - the subject of my dissertation research - improves our ability to confidently implement low-cost, high-fidelity fluid flow models into design processes, aeroelastic simulations, and more.

Reduced-Order Models

Simulating fluids is expensive and easy to get wrong. Weather forecasts require some of the largest computer resources on the planet; a large challenge in designing transportation technologies like cars and airplanes likewise lies in predicting how air and water will interact with the vehicles. The challenge to be accurate becomes all too real when, for example, predicting a hurricane's path can save lives and make sure those who need to evacuate have a chance to do so.

Reduced-order modeling (ROM) is one way that we try to reduce the cost of simulating fluids without sacrificing accuracy. Generally, a more expensive simulation -- and hopefully a more accurate one -- requires the calculation of more, and more complicated, equations. We seek fewer, simpler equations tailored specially for the problems that we want to solve which are very accurate without also being very expensive. This kind of research has been done for decades with promising results, (See the below animations of a lid-driven cavity flow.) but we still struggle to predict when it will work well. Without the ability to reliably trust our reduced-order models, we can't implement them for the amazing cost savings that they promise.

This was the subject of my dissertation research: to develop a way to construct reduced-order models whose accuracy is more reliable to predict. Our hypothesis is that a modal basis which better captures the flow's multiscale dynamics will better perform in a reduced-order model.

The proper orthogonal decomposition (POD) identifies a linear modal basis which spans, optimally in the mean L2 sense, the nonlinear subspace of a provided flow solution. If the provided snapshots are of the fluctuating velocity field, then the POD modes optimally capture the flow's turbulent kinetic energy. One limitation of the POD is thus that it prioritizes large-scale dynamics. However, the inherently multiscale nature of turbulent fluid flows means that dynamically significant, albeit smaller, scales of motion are not adequately captured by the POD basis. This research explores several ways to better identify a modal basis given this multiscale objective.