Physical Sciences and Mathematics Commons^™

Convergence Of The Boundary Integral Method For Interfacial Stokes Flow, Keyang Zhang

Dissertations

Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of discretization points and allows the treatment of complicated interfaces. Despite their popularity, there is no analysis of the convergence of these methods for interfacial Stokes flow. In practice, the stability of discretizations of the boundary integral formulation can depend sensitively on details of the discretization and on the application of numerical filters. A convergence analysis of the boundary integral method for Stokes flow …

Efficient Time-Stepping Approaches For The Dispersive Shallow Water Equations, Linwan Feng

Dissertations

This dissertation focuses on developing efficient and stable (high order) time-stepping strategies for the dispersive shallow water equations (DSWE) with variable bathymetry. The DSWE extends the regular shallow water equations to include dispersive effects. Dispersion is physically important and can maintain the shape of a wave that would otherwise form a shock in the shallow water system.

In some cases, the DSWE may be simplified when the bathymetry length scales are small (or large) in relation to other length scales in the shallow water system. These simplified DSWE models, which are related to the full DSWEs, are also considered in …

Flare Emission Observed In High Resolution And Comparison With Numerical Modeling, Nengyi Huang

Dissertations

As one of the most intense activities on the solar surface, flares have been extensively observed and studied ever since the first report. The standard model of solar flares has been established and commonly accepted. However, many limitations from the researching tools have left some of the problems unsolved or controversial. For example, the density of electrons in the corona is lower than it is required to activate the observed emission in HXR, and the mechanism that these electron beams can penetrate down to lower chromosphere is unclear. Many theoretical scenarios were suggested, and more observations had been in need. …

Calculating Elastic Properties Of Confined Simple Fluids, Christopher D. Dobrzanski

Dissertations

Confinement in nanoporous materials is known to affect many properties of the fluids confined within their pores. The elastic properties are no exception. This dissertation begins with an overview of the relevant literature on ways of obtaining elastic properties of confined fluids. It outlines some fundamental gaps in our understanding. The chapters following address some of these gaps in understanding elastic properties of the confined fluid, in particular, how the shape of the confining pore matters, how supercriticality effects the properties, how an equation of state designed for confined fluids can be used to calculate elastic properties, and if an …