UC Davis

In this dissertation, we develop a numerical simulation framework for multiscale fluid flows in multiple space dimensions. We couple a robust front-capturing approach with an efficient front-tracking scheme; adaptivity is incorporated via a novel adaptive meshing procedure. The work presented is comprised of four articles published in the Journal of Computational Physics. We begin with a summary of the research performed, introducing the problems under consideration and an overview of our framework and its principal components. We summarize the new methods developed, their mathematical formulations and associated algorithmic implementations, and the results obtained. Each of the three subsequent chapters then describes in detail a particular component of the multiscale framework.