Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/gmd-2017-221
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Development and technical paper
25 Oct 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).
A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4, a DG finite element hydrodynamic model, with an application to the thermocline oscillations of Lake Tanganyika
Philippe Delandmeter1, Jonathan Lambrechts1, Vincent Legat1, Valentin Vallaeys1, Jaya Naithani1, Wim Thiery2,3, Jean-François Remacle1, and Eric Deleersnijder4,5 1Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering (IMMC), Avenue Georges Lemaître 4, B-1348 Louvain-la-Neuve, Belgium
2ETH Zürich, Institute for Atmospheric and Climate Sciences, Universitätstrasse 16, 8092 Zürich, Switzerland
3Vrije Universiteit Brussel, Department of Hydrology and Hydraulic Engineering, Pleinlaan 2, B-1050 Brussels, Belgium
4Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering (IMMC) & Earth and Life Institute (ELI), Avenue Georges Lemaître 4, B-1348 Louvain-la-Neuve, Belgium
5Delft University of Technology, Delft Institute of Applied Mathematics (DIAM), Mekelweg 4, 2628CD Delft, The Netherlands
Abstract. The discontinuous Galerkin (DG) finite element method is well suited to the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces.

The mesh vertical movement is determined by means of a conservative Arbitrary Lagrangian–Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level.

The vertically adaptive mesh approach is implemented in the geophysical and environmental flow model SLIM 3D (www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.


Citation: Delandmeter, P., Lambrechts, J., Legat, V., Vallaeys, V., Naithani, J., Thiery, W., Remacle, J.-F., and Deleersnijder, E.: A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4, a DG finite element hydrodynamic model, with an application to the thermocline oscillations of Lake Tanganyika, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2017-221, in review, 2017.
Philippe Delandmeter et al.
Philippe Delandmeter et al.

Model code and software

SLIM v0.4
S. Blaise, B. de Brye, P. Delandmeter, E. Deleersnijder, T. Kärnä, J. Lambrechts, A. Pestiaux, J.-F. Remacle, A. Saint-Amand, B. Seny, C. Thomas, V. Vallaeys, and D. Vincent
https://doi.org/10.5281/zenodo.1002221
Philippe Delandmeter et al.

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Short summary
The discontinuous Galerkin (DG) finite element method is well suited to the modelling of three-dimensional flows exhibiting strong density gradients. Here, a vertical adaptive mesh method is developed for DG finite element methods and implemented into SLIM 3D. This technique increases drastically the accuracy of simulations including strong stratification, without affecting the simulation cost. SLIM 3D is then used to simulate the thermocline oscillations of Lake Tanganyika.
The discontinuous Galerkin (DG) finite element method is well suited to the modelling of...
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