My Research interests lie primarily in analytical fluid dynamics. My main focus is on the theory of traffic flow, in which the motion of cars on a roadway is compared to that of a fluid stream. I am also interested more broadly in hyperbolic conservation laws and collective dynamics. More recently, I have become interested in second order macroscopic models for traffic flow (such as the Aw-Rascle-Zhang model), in which the density and velocity of traffic each have their own (coupled) dynamics. Click below to read a paper I co-authored with my advisor, Dr. Changhui Tan, regarding analysis of first order nonlocal macroscopic models.

During summer 2023, I served as a graduate student intern at UMD ARLIS. With guidance from Dr. James Baeder, our team used machine learning to improve CFD solvers for the Spalart Allmaras (SA) turbulence closure model for Reynolds-Averaged-Navier-Stokes (RANS) equations. While turbulence models for RANS are attractive compared to computationally intractable direct numerical simulation (DNS), current turbulence models perform poorly when adverse pressure gradients (e.g. separated flow) is present. We used Field-Inversion-Machine-Learning (FIML) to produce a neural network correction to the SA model by modifying the turbulence production term. In house mesh generation and flow solvers were computed using the UMD Zaratan HPC cluster (80 Nvidia A100 GPUs!). For the FIML step, adjoint methods are used to compute gradients.

Figure: One sees a recirculating flow in the separated flow region. The nlf-0416 airfoil is experiencing stall due to high angle of attack (20 degrees). SA turbulence model is inaccurate in quantifying loss of lift owing to this phenomenon.