High-Fidelity Numerical Simulation of Shallow Water Waves
Tsunamis impose significant threat to human life and coastal infrastructure. The goal of my dissertation is to develop a robust, accurate, and computationally efficient numerical model for quantitative hazard assessment of tsunamis. The length scale of the physical domain of interest ranges from hundreds of kilometers, in the case of landslide-generated tsunamis, to thousands of kilometers, in the case of far-field tsunamis, while the water depth varies from couple of kilometers, in deep ocean, to few centimeters, in the vicinity of shoreline. The large multi-scale computational domain leads to challenging and expensive numerical simulations. I present and compare the numerical results for different important problems --- such as tsunami hazard mitigation due to presence of coastal vegetation, boulder dislodgement and displacement by long waves, and tsunamis generated by an asteroid impact --- in risk assessment of tsunamis. I employ depth-integrated shallow water equations and Serre-Green-Naghdi equations for solving the problems and compare them to available three-dimensional results obtained by mesh-free smoothed particle hydrodynamics and volume of fluid methods. My results suggest that depth-integrated equations, given the current hardware computational capacities and the large scales of the problems in hand, can produce results as accurate as three-dimensional schemes while being computationally more efficient by at least an order of a magnitude.