Numerical Tests for Parameters When Solving Multi-layer Shallow Water Equations

Hurricanes wreak havoc through coastal communities all over the world. Damage due to wind, rain, and ooding can cause billions of damage in a single, destructive season. By modeling the storm surge for tropical storms, one component of ooding, we can make better informed decisions when taking precautionary action against future storms. In particular, one method of modeling storm surge is using a set of conservation laws that model the physical system, such as the shallow water equations. In this thesis, we are considering the shallow water equations across two layers, or a multi-layer shallow water system. By using the multi-layer shallow water equations instead of the single-layer shallow water equations commonly used in meteorology and other applications, the multi-layer equations aim to capture the dierences in forces driving the movement of water during a surge { distinguishing between a top layer forced by wind and a bottom layer that moves more slowly. In this thesis, I examine the numerically computed eigenspace of the multi-layer shallow water equations needed for the finite volume method driving the conservation law model in order to choose accurate, fast methods of solving for eigenvalues, which will ultimately result in a faster, more accurate numerical method overall for modeling the multi-layer shallow water equations