Nonlinear free-surface flow modeling using volume of fluid (VOF) method

Modeling free-surface flows has many applications in coastal and offshore engineering. It can provide simulations of fluid-body interaction and wave motion. In this study, a two-dimensional flow model is developed to simulate free-surface flows with the presence of complicated boundaries. The concept of volume of fluid (VOF) is employed to treat the movement of the free surface and the partial cell treatment method is used to analyze flows on sloping boundaries. The fluid velocities and pressure are calculated by solving the combined continuity and momentum equations numerically using the finite-difference scheme. The moving free surface is modeled by using the VOF method where the net change of fluid flux and volume fraction of fluid on the surface cell are calculated to update the new position of the free surface. To model free-surface flows on a sloping bottom, a series of revised continuity, momentum, and free-surface equations are derived with the incorporation of a cell's geometric information which specifies the fluid volume fraction of a cell. The model is tested and applied to study the nonlinear free-surface flows generated by an impulsively accelerating plate and propagation of nonlinear shallow-water waves on a flat bottom or over a plane beach as well as their interactions with a vertical wall. The incident wave includes either a solitary wave or a cnoidal wave. The numerical results are compared with existing experimental measurements and other published results. It is found that the numerical results obtained from the present model are in a good agreement with the experimental data and other numerical results for the predictions of free-surface elevation and pressure distribution. The present VOF based flow model is demonstrated to be capable of modeling the nonlinear free-surface flows even when the water depth becomes very small.