Physical Sciences and Mathematics Commons^™

Computational Simulation Of Mass Transport And Energy Transfer In The Microbial Fuel Cell System, Shiqi Ou

Doctoral Dissertations

This doctoral dissertation introduces the research in the computational modeling and simulation for the microbial fuel cell (MFC) system which is a bio-electrochemical system that drives a current by using bacteria and mimicking bacterial interactions found in nature. The numerical methods, research approaches and simulation comparison with the experiments in the microbial fuel cells are described; the analysis and evaluation for the model methods and results that I have achieved are presented in this dissertation.

The development of the renewable energy has been a hot topic, and scientists have been focusing on the microbial fuel cell, which is an environmentally-friendly …

Numerical Methods For Deterministic And Stochastic Phase Field Models Of Phase Transition And Related Geometric Flows, Yukun Li

Doctoral Dissertations

This dissertation consists of three integral parts with each part focusing on numerical approximations of several partial differential equations (PDEs). The goals of each part are to design, to analyze and to implement continuous or discontinuous Galerkin finite element methods for the underlying PDE problem.

Part One studies discontinuous Galerkin (DG) approximations of two phase field models, namely, the Allen-Cahn and Cahn-Hilliard equations, and their related curvature-driven geometric problems, namely, the mean curvature flow and the Hele-Shaw flow. We derive two discrete spectrum estimates, which play an important role in proving the sharper error estimates which only depend on a …

Domain Decomposition Methods For Discontinuous Galerkin Approximations Of Elliptic Problems, Craig Dwain Collins

Doctoral Dissertations

The application of the techniques of domain decomposition to construct effective preconditioners for systems generated by standard methods such as finite difference or finite element methods has been well-researched in the past few decades. However, results concerning the application of these techniques to systems created by the discontinuous Galerkin method (DG) are much more rare.

This dissertation represents the effort to extend the study of two-level nonoverlapping and overlapping additive Schwarz methods for DG discretizations of second- and fourth-order elliptic partial differential equations. In particular, the general Schwarz framework is used to find theoretical bounds for the condition numbers of …

Numerical Analysis Of Convex Splitting Schemes For Cahn-Hilliard And Coupled Cahn-Hilliard-Fluid-Flow Equations, Amanda Emily Diegel

Doctoral Dissertations

This dissertation investigates numerical schemes for the Cahn-Hilliard equation and the Cahn-Hilliard equation coupled with a Darcy-Stokes flow. Considered independently, the Cahn-Hilliard equation is a model for spinodal decomposition and domain coarsening. When coupled with a Darcy-Stokes flow, the resulting system describes the flow of a very viscous block copolymer fluid. Challenges in creating numerical schemes for these equations arise due to the nonlinear nature and high derivative order of the Cahn-Hilliard equation. Further challenges arise during the coupling process as the coupling terms tend to be nonlinear as well. The numerical schemes presented herein preserve the energy dissipative structure …