Our analytical efforts are focused primarily on understanding the fundamental behavior of fluids and complex materials using the tools of partial differential equations, integral equations, and asymptotics. Our goal is to obtain tractable models and rigorous results concerning such phenomena as shock waves, complex fluid instabilities, interface motion, and fluid/structure interactions.
Our computational efforts are aimed at developing high resolution, adaptive tools to simulate fluid flows and heat transfer in complex (and sometimes evolving) geometries, to propagate waves in exterior domains, to determine the elastic and electromagnetic properties of composite materials, to simulate the dynamics and microstructure of complex fluids, and to simulate the interaction of fluids with deformable bodies.
|Computational Stochastics||Dynamics of Complex Fluids|
|Imaging and Heat Flow||Fast Algorithms and PDE libraries|
|Cartesian Embedded Boundary Methods|