Mathematical Sciences Department
Colloquium
Speaker: Dana Ferranti, WPI
Friday, September 8, 2023
11:00 am - 11:50 am
HA209, Forkey Conference Room
Host: Sarah Olson
Title: Simulating bodies immersed in viscous flows: new developments in the Method of Regularized Stokeslets (MRS)
Abstract: The method of regularized Stokeslets (MRS) is a popular numerical method for simulating viscous-dominated flows (a.k.a. Stokes flows) generated by forces distributed over surfaces. Physically, these flows occur at the microscale and are relevant in the study of bacteria/sperm motility, ciliary propulsion, and many more subjects of scientific interest. The method works by replacing point forces with regularized forces, effectively spreading the force in a localized region at the point of application through a Gaussian-like ``blob'' function which depends on a parameter ϵ. In the classic implementation of MRS, the choice of ϵ is chosen for accuracy reasons to be about the same size as the spatial discretization of the surface. This places a practical limit on how small one can make ϵ, and in turn, how small one can make the regularization error. The focus of this talk will be on a variation of the method that replaces the scattered forces and quadrature in the traditional implementation of MRS with a piecewise linear force distribution over a triangulated mesh and analytic integration. The result is an extreme weakening of the dependence of the regularization parameter on the discretization of the surface, as demonstrated through several examples. This talk is intended to be widely accessible to people of different mathematical backgrounds.