A novel CFD algorithm called LEAP is currently being developed by the Kasbaoui Research Group (KRG) using the Immersed Boundary Method (IBM) to describe complex geometries. To validate the algorithm, this research project focused on testing the algorithm in three dimensions by simulating a sphere placed in a moving fluid. The simulation results were compared against the experimentally derived Schiller-Naumann Correlation. Over the course of 36 trials, various spatial and temporal resolutions were tested at specific Reynolds numbers between 10 and 300. It was observed that numerical errors decreased with increasing spatial and temporal resolution. This result was expected as increased resolution should give results closer to experimental values. Having shown the accuracy and robustness of this method, KRG will continue to develop this algorithm to explore more complex geometries such as aircraft engines or human lungs.

High-entropy alloys possessing mechanical, chemical, and electrical properties that far exceed those of conventional alloys have the potential to make a significant impact on many areas of engineering. Identifying element combinations and configurations to form these alloys, however, is a difficult, time-consuming, computationally intensive task. Machine learning has revolutionized many different fields due to its ability to generalize well to different problems and produce computationally efficient, accurate predictions regarding the system of interest. In this thesis, we demonstrate the effectiveness of machine learning models applied to toy cases representative of simplified physics that are relevant to high-entropy alloy simulation. We show these models are effective at learning nonlinear dynamics for single and multi-particle cases and that more work is needed to accurately represent complex cases in which the system dynamics are chaotic. This thesis serves as a demonstration of the potential benefits of machine learning applied to high-entropy alloy simulations to generate fast, accurate predictions of nonlinear dynamics.

This thesis presents the design and simulation of an energy efficient controller for a system of three drones transporting a payload in a net. The object ensnared in the net is represented as a mass connected by massless stiff springs to each drone. Both a pole-placement approach and an optimal control approach are used to design a trajectory controller for the system. Results are simulated for a single drone and the three drone system both without and with payload.

Exploration of icy moons in the search for extra-terrestrial life is becoming a major focus in the NASA community. As such, the Exobiology Extant Life Surveyor (EELS) robot has been proposed to survey Saturn's Moon, Enceladus. EELS is a snake-like robot that will use helically grousered wheels to propel itself forward through the complex terrains of Enceladus. This moon's surface is composed of a mixture of snow and ice. Mobility research in these types of terrains is still under-explored, but must be done for the EELS robot to function. As such, this thesis will focus on the methodologies required to effectively simulate wheel interaction with cohesive media from a computational perspective. Three simulation tools will be briefly discussed: COMSOL Multiphysics, EDEM-ADAMS, and projectChrono. Next, the contact models used in projectChrono will be discussed and the methodology used to implement a custom Johnson Kendall Roberts (JKR) collision model will be explained. Finally, initial results from a cone penetrometer test in projectChrono will be shown. Qualitatively, the final simulations look correct, and further work is being done to quantitatively validate them as well as simulate more complex screw geometries.