Applied Mathematics Department
Illinois Institute of Technology
Modeling and Computation of Moving Boundary Problems
In this talk, I will discuss two moving interface problems. The first one is the classical Hele-Shaw problem. From a computation point of view, the complex fingering morphology due to the Saffman-Taylor instability and the intrinsic slow growth make long-time simulations very expensive. Here I present a time and space rescaling scheme, which can significantly reduces the computation time (especially for slow growth), and enables one to accurately compute the very long-time dynamics of moving interfaces. I will also show some recent results on a curvature weakening model.
The second problem is the modeling of a multi-component vesicle in fluids. This work is motivated by recent experimental results on giant unilamellar vesicles that show mixed multiple lipid components on the surface of a membrane may decompose into coexisting phase domains with distinct compositions. I will derive a thermodynamically consistent model using an energy variation approach. Numerical results suggest that the nonhomogeneous bending, together with the flow, introduces nontrivial vesicle dynamics including, tumbling and wrinkling.
Sponsored by the Department of Mathematical Sciences
Refreshments will be served in the FO 2.604 30 minutes prior to the talk