Date of Award

Spring 1-1-2017

Document Type


Degree Name

Master of Science (MS)


Aerospace Engineering Sciences

First Advisor

Kurt K. Maute

Second Advisor

Georg Pingen

Third Advisor

Brian Argrow


Microscale fluid flows have gained increased attention in recent years. As the physical scale of fluidic devices decreases, rarefaction effects governed by the Knudsen number appear and the continuum assumption is invalid. Fluidic devices designed without the consideration of these effects may, in turn, perform sub-optimally. The goal of this thesis is to present two alternative approaches for modeling flows with finite Knudsen numbers. First, a comparison of governing equations derived from a moment method approach to the Boltzmann Transport Equation is considered. The proposed stabilization scheme is found to be overly diffusive for nonlinear equations, which are expected for higher-order moment equations. As an alternative, the incompressible Navier-Stokes equations are used and a slip boundary condition is proposed to model the non-zero fluid velocity near solid walls that occur at finite Knudsen numbers. The explicit Level Set Method (LSM) is adopted to provide the precise location and orientation of the fluid-solid interface and the eXtended Finite Element Method (XFEM) is used to realize the flow. A ghost penalty stabilization method ensured smooth velocity gradients along the interface. The framework is validated with 2D numerical examples. Finally, 2D and 3D topology optimization examples are studied. For some examples, ignoring the slip boundary leads to considerable design differences and sub-optimal performance.