SLIM2D is used in shallow-water environments where wind and tides are sufficient to keep the water column rather well mixed. It solves the depth-averaged shallow water equations for the surface elevation and the horizontal velocity. When the horizontal flow is mainly unidirectional such as for a well-mixed river, the shallow water equations can be averaged over the section leading to the 1D section-averaged shallow-water equations. SLIM1D consists of linear river segments where variable river width and cross-section are taken into account. River segments can be joined to model a river network with accurate computation of bifurcation by the means of a Riemann solver.
SLIM solves the model equations on an unstructured mesh with the Discontinuous Galerkin finite element method. This approach provides an optimal degree of flexibility both geometrically and functionally as it can accurately represent complex topographies and also model solutions with sharp gradients. Unlike more standard numerical methods, such as finite volumes, it introduces a minimal amount of numerical dissipation and thus preserves small-scale flow features such as recirculation eddies. The model equations can be forced by wind, tides, river discharges and large-scale currents from a global ocean model.
Most coastal areas are significantly influenced by tides. When approaching the coast, the tidal signal tends to amplify, especially in funnel-shaped embayments where the tidal range may reach considerable magnitudes. Combined with the fact that many estuaries and embayments also feature gradually sloping bathymetry, the total area submerged under water may vary significantly during the tidal cycle. To tackle this issues, SLIM2D is equipped with a wetting-drying algorithm that allows it to handle dry areas. The algorithm is based on an implicit time-stepping that combines computational efficiency with local mass conservation. The video below shows the water transport in the Columbia River estuary as modeled by SLIM2D. Dry tidal flats are clearly visible at low tide.