TITLE:
Numerical Investigation of Ocean and Coastal Wave Dynamics: Shallow Water Equation Framework
AUTHORS:
Mohammad Tanzil Hasan, Sudipta Roy
KEYWORDS:
Shallow Water Equations, Bathtub Model, Tsunami Waves, Lax-Wendroff Method, Bathymetry Effects, Wave Propagation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.8,
August
19,
2026
ABSTRACT: This research focuses on the numerical investigation of ocean and coastal wave dynamics using the shallow water equations (SWEs) framework with the bathtub model as a simplified domain. The study employs a MATLAB-based simulation to analyze wave behavior, including propagation, reflection, and wave interference under idealized conditions. The governing equations consist of the continuity equation and the momentum conservation equations, capturing nonlinear wave propagation and interaction governed by the nonlinear shallow water equations. The bathtub model, with its confined geometry, offers a controlled environment for studying key dynamics such as wave resonance, boundary interactions, and energy dissipation. The numerical implementation uses finite difference schemes to discretize the SWEs, ensuring stability and accuracy. Key findings include insights into the influence of initial wave conditions, the role of geometric constraints in amplifying or dissipating wave energy, and the interplay between hydrodynamic forces and boundaries. These results are relevant for understanding storm surges, tidal behavior, and the impact of coastal infrastructure.