I defended my PhD thesis this week, and walked in the graduation ceremony.
The cliff notes for my thesis are that I developed a new framework for topology and shape optimization of strongly coupled fluid-structure interaction problems. I presented 2- and 3-D results using a framework that combines many state of the art numerical methods in applied mathematics and computational mechanics, implemented using various computer science concepts.
The most notable detail is the ability for this framework that I developed to accurately and robustly design real world, nonlinear, 3D multi-physics (fluid-structure) problems. Moreover, I optimize a bio-prosthetic aortic heart valve to reduce human blood damage (a measure of shear) while constraining the pressure drop (simulating being able to move enough blood through the valve).
In addition, this immersed framework allows me to rapidly simulate fully two-way coupled fluid-structure interaction of any image without having to build a body fitted mesh for the contour, which can cut down months of pre-processing for an experienced engineer. Additionally, this work can be combined with multiple interface coupling conditions to simulate two-phase flow, thermal convection, or a combination of multiple conditions.