PDE Modeling and Computation of Moving Interface Problems

Description

In this talk, I will use vesicle dynamics as an example to demonstrate two modeling approaches and discuss challenges in computation. The first part is based on a classical sharp interface approach. I will show the derivation of the model and corresponding interface (boundary) conditions. In the second part, I will present a phase field model by focusing on vesicle expanding or shrinkage, induced by osmotic pressure that arises due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the phase field, a Cahn-Hilliard equation describing the concentration field, and a Stokes equation describing the motion of the vesicle. Conditions for vesicle growth or shrinkage are analyzed via the common tangent construction in the osmotic energy. Finally, I will show some interesting numerical results.