Numerical solution of ocean wave propagation using integrated o-transformation and finite difference methods

This paper provides a novel numerical approach in order to simulate ocean wave propagation, integrating o-transformation with the finite difference schemes. The governing equations are derived from viscous flow theory, specifically the incompressible Navier-Stokes equations under the assumption of negligible viscosity (Euler's equations). The continuity equation represents the conservation of mass and is a fundamental part of fluid dynamics, applicable to both potential flow theory and viscous flow theory, and momentum equations represent the conservation of momentum in the horizontal and vertical directions, respectively. The method enhances accuracy and stability in modeling wave dynamics in deep and transitional waters while effectively handling complex geometries and boundary conditions. Numerical experiments indicate high precision and the capability to capture nonlinear wave behavior, particularly in comparisons with linear and second-order Stokes theory. Stability analyses confirm that the framework maintains reliable results across varying time steps with minimal error growth. This research provides a powerful tool for ocean wave simulation, holding significant implications for marine engineering, environmental studies, and coastal management.