Three students land 2020 NDSEG fellowships

Adam Christopherson

Advisor: Kurt Maute
Lab: Topology Optimization Laboratory

My research focuses on developing strategies for level set XFEM topology optimization based on a relatively new finite element analysis method called finite element exterior calculus (FEEC). While a large number of topology optimization tools rely on the finite element method, FEEC is a different framework in the sense that it bases the finite element method on the calculus of differential forms. FEEC was developed as a powerful structure-preserving analysis method, and has since been studied in the mathematics community and for applications such as computational electromagnetism. However, we have predicted several advantages when applying this method to topology optimization as well given the structure-preserving nature of these finite element discretizations. I am excited to work on this research because it will allow for more robust design optimization when complex physics and design domains are involved. This research is primarily aimed at aerospace applications, but other fields can likely benefit from the framework as well.

Luke Peterson

Advisor: Dan Scheeres
Lab: Celestial and Spaceflight Mechanics Laboratory

I work on a class of higher-dimensional orbits called quasi-periodic orbits or quasi-periodic tori. If we consider the gravitational attraction of the planets as a dynamical system, i.e. a system that evolves over time, then there are special solutions to the system. The 0-dimensional solution is called an equilibrium point: if you start there, you stay put. The 1-dimensional solution is called a periodic orbit: similar to a circle or a loop, if you're on a periodic orbit you can move forward, and you eventually repeat yourself. The 2- and higher-dimensional solutions are called quasi-periodic orbits, and it is these solutions that I study. Quasi-periodic orbits are trajectories that never repeat and, crucially, lie on the surface of a torus. An example of a torus in 2-dimensions is a donut. If these trajectories repeated themselves, they would be periodic, not quasi-periodic. The data that describes quasi-periodic tori is non-unique, in other words, two different sets of data can describe the same quasi-periodic torus. In my time at CU Boulder thus far, I have developed a fundamental representation of quasi-periodic tori. In the remainder of my time at CU, I hope to investigate connections between quasi-periodic orbits for efficient mission design throughout the solar system.

(Photo: Jurnee Murray)

Samantha Sheppard

Advisor: John Farnsworth
Lab: Experimental Aerodynamics Laboratory

In my first year at the University of Colorado Boulder my research focused on the preliminary development of a turbulent synthetic surface layer in a low speed wind tunnel. The continuation of this work will support the development of improved boundary conditions for Large Eddy Simulations (LES). The primary motivation for this work is to improve LES modeling of the Atmospheric Boundary Layer. Moving forward, I will be contributing to a collaborative Strategic Environment Research and Development Program project by conducting flow measurements of flames in a novel sloping wind tunnel to validate and inform computational wildfire models. The aim of this project is to develop improved computational capability to reliably predict wildfire behavior. My work within this project will contribute to the validation of these models as well as extending the current understanding of the development of 3D structures in a finite span flame front and the effect of these structures on the flame propagation.