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 perpendic
ular. 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 atmo
spheric 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 ca
pabilities 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 predict
ing 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.
