Modeling storm surges using discontinuous Galerkin methods
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Storm surges have a devastating impact on coastlines throughout the United States. In order to accurately understand the impacts of storm surges there needs to be an effective model. One of the governing systems of equations used to model storm surges' effects is the Shallow Water Equations (SWE). In this thesis, we solve the SWE numerically by means of a discontinuous Galerkin (DG) method. The DG method provides high-order accuracy and geometric flexibility on unstructured grids. To run the model, we used both implicit and explicit time integration for solving the SWE. Using explicit time integration as our fundamental truth, we found the error norm of the implicit method to be minimal. This study focuses on the impacts of a simulated storm surge in La Push, Washington, which had undergone a beach restoration project. The beach restoration involved altering the bathymetry along the shoreline to prevent overtopping waves from breaching the mainland. To validate the simulations, we ran three benchmark tests. Real bathymetry was used along with real storm and tidal data. We measured the momentum flux of a wave on the existing bathymetry and the new bathymetry to determine if the new bathymetry had less momentum flux. Our results showed there was less momentum flux with the new bathymetry, and therefore the new bathymetry was more resistant to storm surges. After running the model at a high resolution, we modified the grid resolution to vary throughout the domain with a focus on high resolution closer to the shoreline. In our simulation, we also learned of the effects spurious waves can have on the results. Due to boundary conditions, a spurious wave can reflect back into a model and impact the velocity and momentum flux.
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