Abstract
Microfluidic devices are used to process fluids at a small scale. Some of these devices contain physical
obstacles that are used to manipulate the flow of fluid through the device. In our work, we implement a Python program for approximating the velocity of an incompressible fluid over a rectangular domain using the Navier-Stokes equations. Our strategy, which is built primarily on common finite difference methods, allows users to easily add obstacles into the domain and observe their effects on fluid flow. In the first half of the thesis, we describe the derivation, implementation, and benchmarking of our strategy. In the latter half, we describe some numerical experiments that we performed with our program to observe the effects of inclusions on both fluid flow and hydraulic resistance. We compare the hydraulic resistance reported by our program with an analytic approximation. Lastly, we briefly mention some possible expansions on our work.