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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.

1D-2D mesh of the Scheldt
2D-1D mesh of the Schledt river, estuary and its tributaries. SLIM2D is used in the estuary and coastal sea. Upstream of the estuary, the mesh becomes one-dimensional in the fresh tidal river network and ends at the limit of the tidal dominance. The arrows indicated the locations where freshwater discharges are imposed.

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.

Currents as modelled with SLIM2D in the Great Barrier Reef. The use of an unstructured mesh with a 250m resolution and the Discontinuous Galerkin method allows us to simulate small-scale flow features such as recirculation eddies.

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.

To learn more…

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Delandmeter, P., Lambrechts, J., Marmorino, G. O., Legat, V., Wolanski, E., Remacle, J.-F., … Deleersnijder, E. (2017). Submesoscale tidal eddies in the wake of coral islands and reefs: satellite data and numerical modelling. Ocean Dynamics, 67(7), 897–913.
Pham Van, C., de Brye, B., Deleersnijder, E., Hoitink, A. J. F., Sassi, M., Spinewine, B., … Soares-Frazão, S. (2016). Simulations of the flow in the Mahakam river–lake–delta system, Indonesia. Environmental Fluid Mechanics, 16(3), 603–633.
Vincent, D., Karatekin, Ö., Vallaeys, V., Hayes, A. G., Mastrogiuseppe, M., Notarnicola, C., … Deleersnijder, E. (2016). Numerical study of tides in Ontario Lacus, a hydrocarbon lake on the surface of the Saturnian moon Titan. Ocean Dynamics, 66(4), 461–482.
Le Bars, Y., Vallaeys, V., Deleersnijder, É., Hanert, E., Carrere, L., & Channelière, C. (2016). Unstructured-mesh modeling of the Congo river-to-sea continuum. Ocean Dynamics, 66(4), 589–603.
Thomas, C. J., Lambrechts, J., Wolanski, E., Traag, V. A., Blondel, V. D., Deleersnijder, E., & Hanert, E. (2014). Numerical modelling and graph theory tools to study ecological connectivity in the Great Barrier Reef. Ecological Modelling, 272, 160–174.
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de Brye, B., Schellen, S., Sassi, M., Vermeulen, B., Kärnä, T., Deleersnijder, E., & Hoitink, T. (2011). Preliminary results of a finite-element, multi-scale model of the Mahakam Delta (Indonesia). Ocean Dynamics, 61(8), 1107–1120.
de Brye, B., de Brauwere, A., Gourgue, O., Kärnä, T., Lambrechts, J., Comblen, R., & Deleersnijder, E. (2010). A finite-element, multi-scale model of the Scheldt tributaries, river, estuary and ROFI. Coastal Engineering, 57(9), 850–863.
Gourgue, O., Comblen, R., Lambrechts, J., Kärnä, T., Legat, V., & Deleersnijder, E. (2009). A flux-limiting wetting–drying method for finite-element shallow-water models, with application to the Scheldt Estuary. Advances in Water Resources, 32(12), 1726–1739.
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