A Numerical Model for Breaking Waves: The Volume of Fluid Method.

Abstract : This report reviews a numerical model for calculating the evolution of a breaking wave. The model is the combination of a modified version of RIPPLE which was originally developed at Los Alamos National Laboratory (Kothe et al., 1991) and the kappa - epsilon turbulence model. In the model, finite difference solutions to the incompressible Reynolds equations for the mean flow field and the kappa - epsilon equations for the turbulent field are obtained on a nonuniform mesh. The free surface locations are represented by the volume of fluid (VOF) data on the mesh. A two-step projection method is used for the mean flow solutions, aided by the incomplete Cholesky conjugate gradient technique solving the Poisson equation for the mean pressure field. Advections of momentum in Reynolds equations and turbulent kinetic energy and dissipation rate in the kappa - epsilon equations are estimated by the combination of the upwind method and the central difference method. Several numerical examples, including the runup and rundown of nonbreaking and breaking solitary waves, are given. Agreement between the experimental data and the numerical results is very good.

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