Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems

A semi-implicit numerical model for the three-dimensional Navier-Stokes equations on unstructured grids is derived and discussed. The governing differential equations are discretized by means of a finite difference-finite volume algorithm which is robust, very efficient, and applies to barotropic and baroclinic, hydrostatic and nonhydrostatic, and one-, two-, and three-dimensional flow problems. The resulting model is relatively simple, mass conservative, and unconditionally stable with respect to the gravity wave speed, wind stress, vertical viscosity, and bottom friction.