Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 134-144). Available also in a digital version from Dissertation Abstracts.

Thesis (M. Phil.)--University of Hong Kong, 1999. / Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, March 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 186-201).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Chandrajit L. Bajaj. Vita. Includes bibliographical references.

Thesis (Ph.D.)--Montana State University--Bozeman, 2006. / Typescript. Chairperson, Graduate Committee: Durward K. Sobek II. Includes bibliographical references.

Melting and vaporization of solids occur very often in nature and in man-made processes. Many analytical and numerical solutions exist for solving the temperature field in the liquid and solid regions, but inaccuracies persist in tracking the phase change interfaces and the numerical solution of the temperature field is usually cumbersome. The Boundary Element Method is proposed as an accurate, efficient way to solve for the temperature field and the interface positions in a phase change problem involving combined melting and vaporization. When comparing to specific one-dimensional test cases, accurate results arc obtained when using a sufficiently small time step. A comparison is made to existing data from a laser drilling experiment. The anticipated physical effects which occur on semi-infinite and finite domains arc confirmed. Consequently, this method can be used to model natural and industrial phenomena involving phase change. / Master of Science

No description available.

In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary. The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an explicit scheme are proposed. The algebraic form of the implicit scheme is of the same form of the Dirichlet--Neumann method, whereas the explicit scheme can be interpreted as the classical staggered scheme using the splitting of the Dirichlet-Neumann method. The explicit scheme is implemented based on two numerical solvers, a Boundary element method (BEM) solver for the potential flow model, and a finite element method (FEM) solver for the Navier-Stokes equations (NSE). The implementation based on the two solvers is validated using numerical examples. / Graduation date: 2013

In this work two inverse methodologies are developed based on the Green element method for the recovery of contaminant release histories and reconstruction of the historical concentration plume distribution in groundwater. Unlike direct groundwater contaminant transport simulations which generally produce stable and well-behaved solutions, the solutions of inverse groundwater contaminant transport problems may exhibit non-uniqueness, non-existence and instability, with escalation in computational challenges due to paucity of data. Methods that can tackle inverse problems are of major interest to researchers, and this is the goal of this work. Basically, the advection dispersion equation which governs the transport of contaminants can be handled by analytical or numerical methods like the Finite element method, the Finite difference method, the Boundary element method and their many variants and hybrids. However, if a numerical method is used to solve an inverse problem the resulting matrix is ill-conditioned requiring special techniques to be employed in order to obtain meaningful solutions. In view of this we explore the Green element method, which is a hybrid technique, based on the boundary element theory but is implemented in an element by element manner. This method is attractive to inverse modelling because of the fewer degrees of freedom that are generated at each node. We develop two approaches, in the first approach inverse Green element formulations are developed, the ill-conditioned matrix that results is decomposed with the aid of the singular value decomposition method and solved using the Tikhonov regularized least square method. The second approach utilizes the direct Green element method and the Shuffled complex evolutionary (SCE) optimization method. Finally, the proposed approaches are implemented to solve typical problems in contaminant transport with analytical solutions besides those that have appeared in various research papers. An investigation on the capability of these approaches for the simultaneous recovery of the source strength and the contaminant concentration distribution is carried out for three types of sources and they include boundary iv sources, instantaneous point sources and continuous point sources. The assessment accounts for different transport modes, time discretization, spatial discretization, location of observation points, and the quality of observation data. The numerical results demonstrate the applicability and limitations of the proposed methodologies. It is found in most cases that the solutions with inverse GEM and the least squares approach are of comparable accuracy to those with direct GEM and the SCE approach. However, the latter approach is found to be computationally intensive.