An Efficient Hydrodynamic Model for Surface Waves

In the present study, a semi-implicit finite difference model for non-hydrostatic, free-surface flows is analyzed and discussed. The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general, irregular domain of arbitrary scale. At outflow, a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflexation. The equations are solved with the fractional step method where the hydrostatic pressure component is determined first, while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The advection and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach. The resulting model is computationally efficient and unrestricted to the CFL condition. The developed model is verified against analytical solutions and experimental data, with excellent agreement.