Three-dimensional model of navier-stokes equations for water waves

A three-dimensional numerical model based on the complete Navier-Stokes equ ations is developed and presented in this paper. The model can be used for the problem of propagation of fully nonlinear water waves. The Navier-Stoke s equations are first transformed from an irregular calculation domain to a regular one using sigma coordinates. The projection method is used to sepa rate advection and diffusion terms from the pressure terms in Navier-Stokes equations. MacCormack's explicit scheme is used for the advection and diff usion terms, and it has second-order accuracy in both space and time. The p ressure variable is further separated into hydrostatic and hydrodynamic pre ssures so that the computer rounding errors can be largely avoided. The res ulting hydrodynamic pressure equation is solved by a multigrid method. A st aggered mesh and central spatial finite-difference scheme are used. The mod el is tested against the experimental data of Luth et al., and the comparis on shows that higher harmonics can be modeled well. Comparison of the model solutions with the elliptic shoal case confirms that the present model wor ks well for wave refraction and diffraction with strong wave focusing.