Adaptive Mesh Refinement for Simulating Tsunami Propagation with Coriolis Effects in Shallow Water Equations

Abstract

This thesis examines the influence of the Coriolis force on the accuracy and efficiency of shallow water equations (SWEs) simulations utilizing adaptive mesh refinement (AMR). Utilizing the open-source GeoClaw software, we implemented a patch-based mesh refinement strategy to solve the SWEs with complete Coriolis force while considering the case where axis of Earth’s rotation is purely perpendicular. Different forms of SWEs are discussed here which accounts for Coriolis terms while keeping different scenarios about Earth’s rotational axis. The inclusion of the Coriolis force is critical for accurately modeling large-scale oceanic and atmospheric phenomena, as it accounts for the effects of Earth’s rotation on moving bodies of water but for short-duration events, the Coriolis effect might not have enough time to noticeably influence the results. Our approach leverages the capabilities of GeoClaw to dynamically adjust the computational grid, ensuring fine resolution in regions where it is most needed while maintaining computational efficiency in less critical areas. This method allows for precise simulation of complex wave patterns and interactions, which are essential for understanding and predicting the behavior of oceanic waves and currents. The results of this study provide valuable insights into the dynamics of oceanic waves and the effectiveness of AMR in enhancing simulation accuracy. To evaluate the influence of the Coriolis effect on tsunami simulations, we revisited the well-documented case of the Great Japan Tohoku Tsunami. This research not only contributes to the field of computational fluid dynamics but also offers practical applications for coastal management, navigation, and disaster preparedness, particularly in regions prone to tsunamis and other wave-related hazards.