Research

Academic work

Peer-reviewed

Regularized Stokeslet Surfaces, DF, R. Cortez. Journal of Computational Physics, 2024.

Correction
Code: see my Github repository

Dissertation

Regularized Stokeslet Surfaces and a Coupled Oscillator System in Stokes Flow

Numerical methods for Stokes flow

In a number of interesting biological applications, viscous forces are several orders of magnitude greater than inertial forces. For these situations, modelers use the Stokes equations to describe the fluid dynamics. For the first part of my dissertation, I worked on an extension to the method of regularized Stokeslets that would allow for improved accuracy of the method when simulating the motion due to forces distributed on 2D surfaces in Stokes flow.

Coupled oscillators in Stokes flows

The second part of my dissertation concerned the analysis of a coupled oscillator model in Stokes flow. The oscillators were spheres which moved due to an external forcing from a spring-like system. Their motion was coupled through the fluid. This kind of model has been analyzed before in the literature (see here). We showed that the in-phase state can be stabilized through the introduction of either an additional elastic coupling between the oscillators, or “weak inertia” which is effected by modeling the fluid with the unsteady Stokes equations.