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SLIM3D solves the three-dimensional hydrostatic equations under the Boussinesq approximation. The model variables are the 3D velocity, the surface elevation, the salinity and the temperature. The density is obtained by means of an equation of state. SLIM3D uses a mesh composed of triangular prismatic elements that are formed by extruding the 2D unstructured mesh in the vertical direction. The model equations are solved by means of the Discontinuous Galerkin finite element method.

3D mesh
Sketch of the 3D mesh obtained by vertically extruding a 2D triangular mesh. All variables are piecewise linear and discontinuous between elements.

One key aspect in any 3D ocean model is the coupling between the external and internal modes. SLIM3D uses a mode-splitting formulation in which the fast propagating gravity waves are solved in an external 2D mode. That mode can either be discretised explicitly with a small time step or implicitly with a larger time step.

Burdekin mesh
3D mesh used to simulate the sediment plume dynamics of the Burdekine River (Australia). The bathymetry being quite shallow and smooth, sigma layers are sufficient to provide an accurate solution.

In the vertical, SLIM3D allows a combination of z and sigma layers. For rather shallow environments with mild bathymetry gradients, sigma coordinates can be used over the entire water column. For deeper areas with sharp bathymetry gradients, sigma layers are generally used only near the surface while z layers are used in the rest of the domain. The number of z layers can be adapted to better approximate bathymetry gradients.

The accuracy of the mode coupling has been tested on a baroclinic test case described in Ilicak et al. (2012). The domain is a periodic (along the 500km-long boundaries) and closed (along the 160km-long boundaries) channel with a bathymetry of 1000m (exaggerated on the video). The large bottom drag coefficient and asymmetric initial condition trigger baroclinic instabilities in the channel. The 4km mesh resolution is similar to one of typical mesoscale eddy permitting models. SLIM3D is able to reproduce the development of baroclinic eddies, as illustrated by the evolution of the predicted temperature.

To learn more…

Alaerts, L., Dobbelaere, T., Gravinese, P. M., & Hanert, E. (2022). Climate Change Will Fragment Florida Stone Crab Communities. Frontiers in Marine Science, 9, 839767.
Vallaeys, V., Lambrechts, J., Delandmeter, P., Pätsch, J., Spitzy, A., Hanert, E., & Deleersnijder, E. (2021). Understanding the circulation in the deep, micro-tidal and strongly stratified Congo River estuary. Ocean Modelling, 101890.
Duquesne, F., Vallaeys, V., Vidaurre, P. J., & Hanert, E. (2021). A coupled ecohydrodynamic model to predict algal blooms in Lake Titicaca. Ecological Modelling, 440, 109418.
Delandmeter, P., Lambrechts, J., Legat, V., Vallaeys, V., Naithani, J., Thiery, W., Remacle, J.-F., & Deleersnijder, E. (2018). A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika. Geoscientific Model Development, 11(3), 1161–1179.
Vallaeys, V., Kärnä, T., Delandmeter, P., Lambrechts, J., Baptista, A. M., Deleersnijder, E., & Hanert, E. (2018). Discontinuous Galerkin modeling of the Columbia River’s coupled estuary-plume dynamics. Ocean Modelling, 124, 111–124.
Delandmeter, P., Lewis, S. E., Lambrechts, J., Deleersnijder, E., Legat, V., & Wolanski, E. (2015). The transport and fate of riverine fine sediment exported to a semi-open system. Estuarine, Coastal and Shelf Science, 167, 336–346.
Kärnä, T., Legat, V., & Deleersnijder, E. (2013). A baroclinic discontinuous Galerkin finite element model for coastal flows. Ocean Modelling, 61, 1–20.
Kärnä, T., Legat, V., Deleersnijder, E., & Burchard, H. (2012). Coupling of a discontinuous Galerkin finite element marine model with a finite difference turbulence closure model. Ocean Modelling, 47, 55–64.
Comblen, R., Blaise, S., Legat, V., Remacle, J.-F., Deleersnijder, E., & Lambrechts, J. (2010). A discontinuous finite element baroclinic marine model on unstructured prismatic meshes: Part II: implicit/explicit time discretization. Ocean Dynamics, 60(6), 1395–1414.
Blaise, S., Comblen, R., Legat, V., Remacle, J.-F., Deleersnijder, E., & Lambrechts, J. (2010). A discontinuous finite element baroclinic marine model on unstructured prismatic meshes: Part I: space discretization. Ocean Dynamics, 60(6), 1371–1393.
White, L., Legat, V., & Deleersnijder, E. (2008). Tracer Conservation for Three-Dimensional, Finite-Element, Free-Surface, Ocean Modeling on Moving Prismatic Meshes. Monthly Weather Review, 136(2), 420–442.
White, L., Deleersnijder, E., & Legat, V. (2008). A three-dimensional unstructured mesh finite element shallow-water model, with application to the flows around an island and in a wind-driven, elongated basin. Ocean Modelling, 22(1–2), 26–47.
White, L., & Deleersnijder, E. (2007). Diagnoses of vertical transport in a three-dimensional finite element model of the tidal circulation around an island. Estuarine, Coastal and Shelf Science, 74(4), 655–669.