A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Can a Broader Education Narrow the Gap? Evidence on Non-Academic Features of Schooling

Empirical studies of education programs and systems, by nature, rely upon use of student outcomes that are measurable. Often, these come in the form of test scores. However, in light of growing evidence about the long-run importance of other student skills and behaviors, the time has come for a broader approach to evaluating education. This dissertation undertakes experimental, quasi-experimental, and descriptive analyses to examine social, behavioral, and health-related mechanisms of the educational process. My overarching research question is simply, which inside- and outside-the-classroom features of schools and educational interventions are most beneficial to students in the long term? Furthermore, how can we apply this evidence toward informing policy that could effectively reduce stark social, educational, and economic inequalities?

The first study of three assesses mechanisms by which the Fast Track project, a randomized intervention in the early 1990s for high-risk children in four communities (Durham, NC; Nashville, TN; rural PA; and Seattle, WA), reduced delinquency, arrests, and health and mental health service utilization in adolescence through young adulthood (ages 12-20). A decomposition of treatment effects indicates that about a third of Fast Track’s impact on later crime outcomes can be accounted for by improvements in social and self-regulation skills during childhood (ages 6-11), such as prosocial behavior, emotion regulation and problem solving. These skills proved less valuable for the prevention of mental and physical health problems.

The second study contributes new evidence on how non-instructional investments – such as increased spending on school social workers, guidance counselors, and health services – affect multiple aspects of student performance and well-being. Merging several administrative data sources spanning the 1996-2013 school years in North Carolina, I use an instrumental variables approach to estimate the extent to which local expenditure shifts affect students’ academic and behavioral outcomes. My findings indicate that exogenous increases in spending on non-instructional services not only reduce student absenteeism and disciplinary problems (important predictors of long-term outcomes) but also significantly raise student achievement, in similar magnitude to corresponding increases in instructional spending. Furthermore, subgroup analyses suggest that investments in student support personnel such as social workers, health services, and guidance counselors, in schools with concentrated low-income student populations could go a long way toward closing socioeconomic achievement gaps.

The third study examines individual pathways that lead to high school graduation or dropout. It employs a variety of machine learning techniques, including decision trees, random forests with bagging and boosting, and support vector machines, to predict student dropout using longitudinal administrative data from North Carolina. I consider a large set of predictor measures from grades three through eight including academic achievement, behavioral indicators, and background characteristics. My findings indicate that the most important predictors include eighth grade absences, math scores, and age-for-grade as well as early reading scores. Support vector classification (with a high cost parameter and low gamma parameter) predicts high school dropout with the highest overall validity in the testing dataset at 90.1 percent followed by decision trees with boosting and interaction terms at 89.5 percent.