In my day job, I am a postdoctoral researcher at the National Renewable Energy Lab. On the whole, my work concerns using numerical simulations for systems engineering for wind and renewable energy. The postdoc is still developing, but publications and research summaries should- eventually- be found here.
Before that I was a Ph.D. student. I worked on researching advanced numerical methods for computational fluid dynamics. The topic of my dissertation is error control for chaotic equations. When equations are solved using a computer, they have to be represented "discretely", or finitely. Think of the difference between a digital photograph of a landscape and looking out at the landscape. With a good camera, the photograph represents the scene well, but if you zoom in enough, small details, usually unimportant, blur into each other at the scale of pixels. In real life, you can zoom in with a spyglass– or with the lens from a spy satellite for that matter– and still see ever more minute details.
The problem with discrete representation of physics is that, well, the details matter. For systems that aren't chaotic, this means that "stabilization" is often necessary to sort out and account for the missing stabilizing effect of the blurred physics that are smaller than the computational physics equivalent of pixels. Luckily, we're getting pretty good at accounting for this fact, and the research for my masters thesis– and this paper that is based on it– looked at one particular aspect of how this process of stabilization sweeps physical details under the rug.
For chaotic systems, on the other hand, the devil is truly in the details. Chaotic systems are fundamentally unpredictable. This is why we don't know exactly where hurricanes will end up, for instance: the tiniest details can have a big impact on the macroscopic behavior of a system. When we blur the details of a chaotic simulation, we are missing information, just like in a non-chaotic simulation. But we also have to account for the fact that the true microscopic behavior, hidden behind the blur, could have any number of unaccounted macroscopic effects in the long term!
My Ph.D. project does a few things for these types of systems. I look in particular at the subset of chaotic problems that have meaningful long-term averages, like the drag on an aircraft in a low-speed, high angle-of-attack cruise or the power extraction of a wind farm over some period of time in consistent ambient conditions. In this realm, "blur" manifests two forms of error, which I work to theoretically and experimentally quantify. Moreover, I find a way to nearly optimally account for these errors so that– even though a system is unknown (before simulating it) and unpredictable– we can get very good bang for our buck in terms of accurately describing the physics with a finite and constrained amount of computational resources.
In the posts in this section, I will have some plain-language to informal research discussion of these research topics and other topics that I find interesting or worth remembering & sharing.