Numerical modeling of extended mild slope equations

Waves transform from deep water to the shallow water. These transformations occur as a result of wave refraction, wave diffraction, wave shoaling, reflection, dissipation due to wave breaking and bottom friction. A numerical model has been developed to simulate these transformations. Nonlinear parabolic mild slope equation and extended mild slope equations have been used in the solution of the numerical model. Nonlinear celerity and group velocity have been included in the solution of the extended mild slope equation. Finite difference and finite volume methods have been used in the solution of the numerical model. Mac Cormack Method and Point Gauss Seidel Method have been applied together in the proposed new solution approach. The numerical model has been tested on the semicirular shoaling, elliptic shoaling and shore parallel breakwater diffraction. Model has been applied to Fethiye Bay and Obaköy coastal areas in Turkish coastline.