A conservative unstructured staggered grid scheme for incompressible Navier-Stokes equations

A finite-volume formulation is proposed to solve the three-dimensional, non-hydrostatic Navier-Stokes equations on an unstructured, staggered, z-lever grid, with the goal of simulating non-hydrostatic processes in the free-surface flows. The advection and diffusion terms in the momentum equation are discretized explicitly with the Eulerian scheme, which has the attractive property of being conservative. An integral method of the top- layer pressure is applied to account for the full effects of non-hydrostatic pressure at the free-surface layer. It is shown that the results obtained with a small number of vertical layers (e.g., 2-3 layers) are in good agreements with experimental data or analytical solutions, demonstrating the efficiency and accuracy of the model in simulating a range of free-surface flow problems including wave motion and tide-induced motion.