Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds

Coastal areas are regions of high population density and urbanization. These areas are highly vulnerable to inundation and flooding not only because of hurricane storm surge, but also because of the torrential rainfall that often accompanies hurricanes. In order to accurately predict the extent of damage such an event might cause, any model that is used to simulate this process needs to couple rainfall with storm surge. The works that have tried to address this issue have mostly used a unidirectional coupling technique, where one of the following two approaches is taken. In the first approach, a hydrology model is used in the domain of interest and storm surge is incorporated in the domain as a boundary condition. In the second approach, a storm surge model is used in the domain of interest and rainfall is incorporated in the domain as a river inflow boundary condition. Neither of these approaches allows the rainwater and the surge water to interact bidirectionally. In order to improve on those efforts, in this dissertation, we develop a comprehensive framework for modeling flooding in coastal watersheds. We present an approach to decompose a watershed into multiple sub-domains depending on the dynamics of flow in the region. We use different simplifications of the shallow water equations on different sub-domains to gain computational efficiency without compromising on physical accuracy. The different sub-domains are coupled with each other through numerical fluxes in a discontinuous Galerkin framework. This technique allows for a tight coupling of storm surge with rainfall runoff, so that the flooding that occurs is truly influenced by the nonlinear interaction of these two processes. We present numerical tests to validate and verify the methods used for modeling flow in different sub-domains as well as the techniques used for coupling different sub-domains with each other.