Date(s) - 22/11/2016
11 h 00 min - 12 h 00 min
Free boundary/moving interface problems are challenging both theoretically and numerically. In this general talk, I will introduce some application examples and corresponding differential equations models. The applications include Stefan problems of unstable crystal growth; drop spreading, and multi-phase flows. Then I will give a brief review of numerical methods for solving those challenging problems, particularly Cartesian grid method such as Peskin’s Immersed Boundary (IB) method, the Immersed Interface Method (IIM), Augmented IIM, and Immersed finite element method (IFEM) developed by myself.
Another major component in solving free boundary/moving interface problems is how to evolve the interface. In our approach, both the front tracking and the level set methods are used. The level set method is simple and robust and can handle topological changes for any dimensions. I am going to discuss some issues about how to combine the level set method with IIM to achieve high order accuracy.
If time allows, I will introduce some recent work Stokes and Darcy and Navier-Stokes and Darcy coupling problems for fluid structure interactions between a fluid flow and a porous media.