I am in my fifth year of a PhD in the Mathematical Sciences Department at Michigan Tech, but my time with Tech begins in 2015. I graduated with a dual degree in mathematics with an applied and computational concentration and chemical engineering in spring of 2019. I then began the applied and computational mathematics master’s program at Tech in the following Fall.
Through chemical engineering training, I developed a fascination with fluid dynamics and related transport phenomena. In my mathematics courses, I learned how much I enjoy programming and analyzing numerical methods for approximating the solution equations that model these phenomena. I count myself extremely fortunate not only that these interests overlap, but that our department has researchers in this field. Thus, I almost immediately began research work with Dr. Alexander Labovsky.
Fluid flow can be one of two main regimes, which each have important applications: turbulent and laminar flow. Turbulent flow, which is characterized by fast, chaotic motion, is crucial in many real-world applications from wing and autobody design to climate and weather modeling. Physical experiments, while vital, are incredibly expensive to perform. Thus, there is a need for numerical simulation to reduce the number of simulations required in a development cycle. Unfortunately, turbulence is famously difficult to simulate on a computer: For example, in order to resolve the flow around a whole airplane wing, one needs to resolve the motion of the fluid down to the tenths of an inch.
Thus, there exists a class of turbulence models which aim not to approximate the fluid flow exactly, but to approximate the main features of the flow without resolving the flow on such a fine scale. However existing turbulence models are often either 1) take too long to compute or 2) are not accurate enough. Building on the work of my advisor, I have investigated a novel (as of 2020) class of turbulence models which are much more accurate while being only slightly more expensive to compute. We have also applied these models in more complicated situations such as fluids which are interacting with one another or fluids which are also subject to electromagnetic forces.
