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« Shallow Water Analytic Solutions for Hydraulic and Environmental Studies »
The shallow water equations (also known as “Saint-Venant equations”) describe very accurately phenomenon such as the overland flow at the surface of a field or the flow in a river. Because they cannot be solved easily, computer codes are used. These codes are usually validated by comparing the simulations to field or laboratory measurements. Another truth exists.
The comparison to analytic solutions: an underused approach
In fact, if no general solution to the shallow water equations is known, exact solutions (also said analytic solutions) are known for specific cases. By comparing the numeric results to these specific cases, it can be ensured that the software gives the right results.
These specific cases have been published over several decades. In other words, they are scattered in the scientific literature and, hence, difficult to access. This explains that the comparison of numeric results to analytic solutions is an underused approach.
SWASHES: the truth according to Saint-Venant
There are several tens of (semi-)analytic solutions. The ones currently included into SWASHES already cover a wide range of flows: sub-critical, super-critical, shock, dam break, permanent or transitory flows, dry-wet transition, with or without friction, with or without rain, in 1D or 2D, etc. Not to use this approach is missing the truth according to the Saint-Venant equations.
SWASHES: the quality assurance of your simulations
Developed in collaboration with the laboratory of mathematics of the University of Orléans (Mapmo), SWASHES gathers analytic and semi-analytic solutions to the shallow-water equations. SWASHES generates the initial conditions and the results to be found. Will your code give the proper result?
Currently, SWASHES includes about thirty solutions covering very diverse flow conditions. Collected from the literature, they have been re-written with the same formalism and coded into the software SWASHES. Hence, they are easy to understand, concentrated into a single piece of software, and available to everyone. By choosing the solutions the closest to the type of flow you want to simulate, you can build a benchmark to test your code.
An example of use: FullSWOF
SWASHES allows ensuring the quality of the results produced by FullSWOF.
The comparison to analytic solutions is carried out at two stages: during the development and during the use by a third party.
During the development. To validate every new version of FullSWOF, a benchmark script compares the results of the new version with the results of the previous one. If there is no difference, the changes to the code did not affect the accuracy of the computation. If differences are reported, it is check the results are improved. In practice, this approach allowed for: - correct bugs before the software release; - alter the order of instructions to limit the propagation of computation errors.
During the first use by a third party. After download and installation, the user of the code is advised to launch the benchmark script. If no difference is reported, it means FullSWOF gives results identical on the user’s computer and on the developers’ computer. The computation reproducibility is ensured.
click on the thumbnail to access the full picture or the video
Test case « Short channel with smooth transition then shock ». Water heights of the analytic solution and according to FullSWOF_2D.
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Test case « Dam break on a dry surface ». Water heights of the analytic solution and according to FullSWOF_1D.
click on the thumbnail to access the full picture or the video
Test case « Planar surface in a paraboloid ». Water heights of the analytic solution and according to FullSWOF_1D.
SWASHES: a free source code
SWASHES is a free software distributed under the license CeCILL-V2 (GPL-compatible). Hence, you can access to all source code (in C++), and are free to use it, to modify it and to redistribute it as long as you include a citation.
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