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SUMMARYA numerical technique is presented for the approximation of vertical gradient of the non-hydrostatic pressure arising in the Reynolds-averaged Navier-Stokes equations for simulating non-hydrostatic freesurface ows. It is based on the Keller-box method that take into account the e ect of non-hydrostatic pressure with a very small number of vertical grid points. As a result, the proposed technique is capable of simulating relatively short wave propagation, where both frequency dispersion and non-linear e ects play an important role, in an accurate and e cient manner. Numerical examples are provided to illustrate this; accurate wave characteristics are already achieved with only two layers.

SUMMARYThis paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied ows as well. Rapidly varied ows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden ow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the e ciency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied ows, as well as in expansions as in contractions. In ow expansions, a numerical approximation is applied that is consistent with the momentum principle. In ow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under su ciently smooth conditions they converge to the same solution. The resulting method is very e cient for the simulation of large-scale inundations.