A three-dimensional mathematical model for free surface flow based on the Reynolds-averaged Navier-Stokes equations is developed in a sigma co-ordinate system. The time-splitting method is used to separate advection and diffusion terms from the pressure terms in the governing equations. The pressure variable is further separated into hydrostatic and hydrodynamic pressures so that the computer rounding errors can be largely avoided. The resulting hydrodynamic pressure equation is solved by a multigrid method, while the hydrostatic pressure equations are solved very efficiently by an Alternating Direction Implicit (ADI) scheme. The convection terms are discretized by the Roe's scheme of second-order accuracy. A staggered mesh is used. The model is tested against available analytical solutions and experimental data. Good agreement has been achieved. RÉSUMÉUn modèle mathématique tridimensionnel pour les écoulements a surface libre, basé sur les equations de Navier Stokes en moyenne de Reynolds, est développé dans un système de coordonnées sigma. La methode des pas fractionnaires en temps est employee pour séparer les termes de convection et de diffusion des termes de pression dans les equations. La pression est ensuite séparée en pression hydrostatique et dynamique pour éviter en grande partie les erreurs d'arrondis de Fordinateur. L'équation resultante de la pression dynamique est résolue par une methode multigrille, alors que les equations de la pression hydrostatique sont résolues tres efficacement par un schema implicite de directions alternées (ADI). Les termes de convection sont discrétisées suivant Ie schema de Roe du second ordre. Le maillage est en quinconce. Le modèle est confronté a des solutions analytiques et des données expérimentales disponibles. Un bon l'accord a été observe.
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