Numerical Modeling of Nonlinear Water Waves with Sigma Coordinate and Layer Thickness Optimization

This paper presents a numerical model for simulating fully dispersive, nonlinear water waves in coastal areas. A finite difference method based on the Keller-Box scheme is used to solve the incompressible Euler equations with the free-surface boundary conditions. The sigma coordinate transformation maps the irregular physical domain with the wavy free surface and the uneven bottom to a rectangular computation domain. A pressure correction technique is utilized in this study, which splits the numerical procedure into hydrostatic and non-hydrostatic phases. An analytical dispersion relationship is derived from the discretized, linearized governing equations for layer thickness optimization. Numerical tests are presented to verify the model and compare with the analytical dispersion relationship.