This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit integration schemes such as described by Leendertse (1967) and Casulli(1990) but that can be applied to problems that include large gradients as well. Large gradients are encountered in hydraulic jumps and bores due to dam breaks. Also flooding of dry land or tidal flats can be considered as a large gradient problem. Near such gradients conservation properties become crucial. The scheme described here combines the efficiency of staggered grids with conservation properties that are similar to Godunov methods.
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