Fast 3D Simulation of Nonhydrostatic Flows Using a Modified Ghost-Cell Free-Surface Pressure Treatment

Abstract

Treatment of the free-surface pressure boundary (FSPB) remains a challenge for the three-dimensional (3D) nonhydrostatic hydrodynamic models using a vertical staggered-grid variable arrangement. Through the tests of the small-amplitude wave, it was found that the pressure of the top layer of the vertical grid is semihydrostatic for vertical staggered-grid nonhydrostatic models. Based on this finding, a modified ghost-cell FSPB treatment is proposed and a fully nonhydrostatic staggered-grid model developed. The new method is simple and easy to implement, and has the self-calibration property of its parameters. The model was further tested using a laboratory experiment of nonlinear waves propagating over a bar toward a beach. Sensitivity studies of model parameters and grid scales were performed. The vertical staggered-grid model using the new FSPB treatment is shown to require only coarse vertical grids to achieve accurate simulations of nonhydrostatic free-surface flows.