Research

I am interested in the numerical analysis, simulation, and visualization of dynamical systems, particularly those with physical applications.

Current

  • Reach Set Computation
  • Traffic management of low-flying UAS is under current development by the FAA and NASA, among others. To be effective, this traffic management should itself be unmanned. This requires an established motion protocol that depends on real-time information about UAS trajectories. My research with Abhishek Halder involves fast and parallelized computation of ellipsoidal outer-approximations of reachable tubes that account for uncertainties in measurement, control, and wind conditions. Such computation must in part be conducted in the 12-dimensional state space in which the dynamics of an aerial vehicle are described. Below are animated examples of reach set computation in two and three dimensions, respectively.

    2D Reach Set 3D Reach Set

Past

  • Study of Transonic Small Disturbance Equation
  • For my undergraduate senior thesis I performed a study of the computation of tranonic flow about a 2D airfoil using the transonic small disturbance (TSD) equation using mixed differencing under the mentorship of Dongwook Lee. Transonic flow is that for which some regions of the flow are subsonic, sonic, and supersonic, typically between Mach 0.7 and Mach 1.2. For the realms in which it is accurate, the TSD approximation is favorable because it can be used to obtain solutions faster than many current computational fluids techniques. I used published results and the FLASH code's full Euler equation solutions to analyze the accuracy of the approximation and found that the approximation was very good in certain cases and unstable in others. This study required thorough understanding of computational fluid dynamics and finite differencing methods, as well as proficiency in both Matlab and Fortran.