Tear film modeling in 1D and 2D moving geometry with high-order methods.

摘要

This thesis deals with an interesting application of mathematics, tear film dynamics. Our goal is to understand and simulate the various observed tear film behaviors, such as film cooling, black line formation and lipid patterns etc. During this process, we build models to describe the fluid dynamics for several blink cycles, experiment on the choices of parameters, compare the simulation with in vivo observation, and develop innovative numerical algorithms.