Abstract

Hydrodynamics at small scales are synonymous in many geophysical, medical, industrial, and biophysical applications. Such flows are modeled with the linear incompressible Stokes equations. Computational challenges arise when the Stokes equations must be solved in a complex geometry, with complex boundary conditions, or both. Boundary integral equations are a powerful reformulation of the Stokes equations that simplify the geometry through a dimension reduction, and automatically satisfy different boundary conditions and far field conditions. I will describe some numerical tools that accurately solve boundary integral equations, and then apply these tools to two different applications. The first application is the dynamics of semipermeable and multicomponent vesicles under strong confinement. The second application is transport in eroded porous media. If time permits, I will show a new method to simulate diffusive processes in unbounded complex geometries. This is joint work with Yuan-Nan Young, Ashley Gannon, Nick Moore, Jake Cherry, Alan Lindsay, and Shang-Huan Chiu.

WebEx Link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m1a7731e4f747062d17af5e20893fb418