\contentsline {chapter}{List of Figures}{iii}{chapter*.2}
\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}
\contentsline {chapter}{\numberline {2}Mathematical Model Description}{3}{chapter.2}
\contentsline {section}{\numberline {2.1}Equations}{3}{section.2.1}
\contentsline {section}{\numberline {2.2}Simplifications}{5}{section.2.2}
\contentsline {section}{\numberline {2.3}Closure Relations}{5}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}Friction Slope}{5}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}Sediment Transport Rate}{5}{subsection.2.3.2}
\contentsline {subsection}{\numberline {2.3.3}Secondary Flow Terms}{7}{subsection.2.3.3}
\contentsline {subsection}{\numberline {2.3.4}Volume Fraction Content at the Interface}{7}{subsection.2.3.4}
\contentsline {chapter}{\numberline {3}Model Characterization}{9}{chapter.3}
\contentsline {section}{\numberline {3.1}Hyperbolicity of a 2D System of Equations}{9}{section.3.1}
\contentsline {section}{\numberline {3.2}Decomposition of the System Equations}{9}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Decomposition of the Sediment Transport Rate}{10}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}Secondary Flow Terms}{10}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}Substitution and Expansion}{11}{subsection.3.2.3}
\contentsline {section}{\numberline {3.3}Matrix-Vector Formulation}{12}{section.3.3}
\contentsline {section}{\numberline {3.4}Implementation in Delft3D}{13}{section.3.4}
\contentsline {chapter}{\numberline {4}Results}{15}{chapter.4}
\contentsline {section}{\numberline {4.1}2D Eigenvalue Analysis}{15}{section.4.1}
\contentsline {section}{\numberline {4.2}Implementation Test}{17}{section.4.2}
\contentsline {section}{\numberline {4.3}2D test case}{21}{section.4.3}
\contentsline {chapter}{\numberline {5}Discussion and Further Research}{23}{chapter.5}
\contentsline {chapter}{\numberline {6}Conclusion}{25}{chapter.6}
\contentsline {chapter}{\numberline {7}References}{27}{chapter.7}
\contentsline {chapter}{\numberline {A}Changes to Delft3D}{29}{appendix.A}