Modeling Flows at the Microscale: a Computational Approach

Abstract

The interaction of flexible structures with a surrounding fluid is at the core of many systems in biology, as in the motion of sperm in the reproductive tract and mucus transport in the lungs. The partial differential equations that describe these systems are the incompressible Stokes equations for fluid velocity. While these equations are linear, their coupling with boundaries, that move at the velocity that evolves from their solution, makes the whole system nonlinear. Numerical approaches such as finite element or finite difference methods rely on discretizing the fluid domain. Like boundary element methods, here we will investigate an approach, the method of Regularized Stokeslets, that does not discretize the surrounding domain but exploits the existence of fundamental solutions or Green’s functions. This allows a surprisingly straightforward and easy-to-implement computational method that can capture fluid-structure interactions at the microscale. The background required for this minicourse is familiarity with ordinary differential equations some basic partial differential equations and programming experience (Matlab).

Prof. Lisa J. Fauci.