Numerical simulation of free surface flow using a three-dimensional numerical model

Abstract

In this study, three-dimensional hydrodynamic pressure model for free surface flows using a normalized vertical coordinate system is presented. Numerical models of free surface flow are developed to calculate the velocity components, the free surface elevations in the following three steps. At the first step, the vertical momentum equations are discretized by using an implicit method over the vertical direction. In the second step, the discrete horizontal momentum equations are projected on to the free surface equation. The predictor-corrector step method is used to calculate variations of free surface elevation and velocity. Finally, the hydrodynamic pressure and final velocity field are calculated. As the vertical velocity is not taken into account at the previous step, the velocity field may not satisfy the local mass conservation at each computational grid cell. In this step, the velocities and the free surface elevation obtained from the previous step are corrected to conserve the local mass balance by considering the hydrodynamic pressure in conjunction with the continuity equation. The developed model is applied to propagation and subsequent run-up process of nearshore solitary wave around a circular island carried out by Coastal Engineering Research Center (CERC), US Army Corps of Engineers. Computed results are then compared with laboratory measurements. Very reasonable agreements are observed.