Browsing this site requires the installation and use of cookies on your computer
Know more
Know more
Our use of cookies
Cookies are a set of data stored on a user’s device when the user browses a web site. The data is in a file containing an ID number, the name of the server which deposited it and, in some cases, an expiry date. We use cookies to record information about your visit, language of preference, and other parameters on the site in order to optimise your next visit and make the site even more useful to you.
To improve your experience, we use cookies to store certain browsing information and provide secure navigation, and to collect statistics with a view to improve the site’s features. For a complete list of the cookies we use, download “Ghostery”, a free plug-in for browsers which can detect, and, in some cases, block cookies.
Ghostery is available here for free: https://www.ghostery.com/fr/products/
You can also visit the CNIL web site for instructions on how to configure your browser to manage cookie storage on your device.
In the case of third-party advertising cookies, you can also visit the following site: http://www.youronlinechoices.com/fr/controler-ses-cookies/, offered by digital advertising professionals within the European Digital Advertising Alliance (EDAA). From the site, you can deny or accept the cookies used by advertising professionals who are members.
It is also possible to block certain third-party cookies directly via publishers:
Cookie type
Means of blocking
Analytical and performance cookies
Realytics Google Analytics Spoteffects Optimizely
Targeted advertising cookies
DoubleClick Mediarithmics
The following types of cookies may be used on our websites:
Mandatory cookies
Functional cookies
Social media and advertising cookies
These cookies are needed to ensure the proper functioning of the site and cannot be disabled. They help ensure a secure connection and the basic availability of our website.
These cookies allow us to analyse site use in order to measure and optimise performance. They allow us to store your sign-in information and display the different components of our website in a more coherent way.
These cookies are used by advertising agencies such as Google and by social media sites such as LinkedIn and Facebook. Among other things, they allow pages to be shared on social media, the posting of comments, and the publication (on our site or elsewhere) of ads that reflect your centres of interest.
Our EZPublish content management system (CMS) uses CAS and PHP session cookies and the New Relic cookie for monitoring purposes (IP, response times).
These cookies are deleted at the end of the browsing session (when you log off or close your browser window)
Our EZPublish content management system (CMS) uses the XiTi cookie to measure traffic. Our service provider is AT Internet. This company stores data (IPs, date and time of access, length of the visit and pages viewed) for six months.
Our EZPublish content management system (CMS) does not use this type of cookie.
For more information about the cookies we use, contact INRA’s Data Protection Officer by email at cil-dpo@inra.fr or by post at:
INRA 24, chemin de Borde Rouge –Auzeville – CS52627 31326 Castanet Tolosan CEDEX - France
« 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.
click on the thumbnail to access the full picture or the video
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.
The SWASHES forge allows centralizing the developments.
The modular structure of SWASHES makes it easy to add a new analytic solution. If you redistribute a modified version of SWASHES, it should be under the license CeCILL-V2 and must carry a new name.
In practice, the easiest way to distribute your improvements to the community is to add directly your solutions into SWASHES: Contact us at swashes.contact@listes.univ-orleans.fr.
Abily M., Delestre O., Amoss L., Bertrand N., Richet Y., Duluc C.-M., Gourbesville P., Navaro P. (2015). Uncertainty related to high resolution topographic data use for flood event modeling over urban areas : Toward a sensitivity analysis approach. In, N. Champagnat, T. Lelièvre, A. Nouy (Eds). ESAIM Proceedings and Surveys. 48: 385-399. http://www.esaim-proc.org/articles/proc/pdf/2015/01/proc144818.pdf
Bustamante C. A. , Power H., Nieto C., Florez W. F. (2015). Solution of two-dimensional Shallow Water Equations by a localized Radial Basis Function collocation method. 1st Pan-American Congress on Computational Mechanics. International Association for Computational Mechanics. Buenos Aires, April 27-29. http://congress.cimne.com/panacm2015/admin/files/fileabstract/a274.pdf
Delestre O., Abily M., , Cordier F., Gourbesville P., Coullon H. (2015) Comparison and Validation of Two Parallelization Approaches of FullSWOF_2D Software on a Real Case. Advances in Hydroinformatics. Simhydro 2014. Part 2, pp. 395-407, Springer. DOI: 10.1007/978-981-287-615-7_27
Delestre O., Razafison U. (2015). Numerical Scheme for a Viscous Shallow Water System Including New Friction Laws of Second Order: Validation and Application. Advances in Hydroinformatics. Simhydro 2014. Part 1, pp. 227-239, Springer. DOI: 10.1007/978-981-287-615-7_16
Fang K., Sun J., Liu Z. Yin J. (2015). A non-hydrostatic model for water waves in nearshore region. Advances in Water Science, 26(1): 114-122. (in Chinese). DOI: 10.14042/j.cnki.32.1309.2015.01.015
Gunawan P. H., Lhébrard X. (2015). Hydrostatic relaxation scheme for the 1D shallow water - Exner equations in bedload transport. Computers & Fluids, 121: 44–50. DOI : 10.1016/j.compfluid.2015.08.001
Le M.-H., Cordier S., Lucas C., Cerdan O. (2015). A faster numerical scheme for a coupled system modeling soil erosion and sediment transport. Water Resources Research, 51(2): 987–1005. DOI: http://dx.doi.org/10.1002/2014WR015690
Ma Q., Abily M., Vo. N. D., Gourbesville P. (2015). High resolution rainfall-runoff simulation in urban aera: Assessment of Telemac-2D and FullSWOF-2D. E-proceedings of the 36th IAHR World Congress. 28 June – 3 July, 2015, The Hague, the Netherlands. http://89.31.100.18/~iahrpapers/84826.pdf
Minatti L. (2015). A well-balanced FV scheme for compound channels with complex geometry and movable bed. Water Resources Research. 51(8):6564–6585. DOI: 10.1002/2014WR016584
Minatti L., De Cicco P. N., Solari L. (2015). Second Order Discontinuous Galerkin scheme for compound natural channels with movable bed. Applications for the computation of rating curves, Advances in Water Resources, In Press. DOI: http://dx.doi.org/10.1016/j.advwatres.2015.06.007
Pongsanguansin T., Maleewong M.,Mekchay K. (2015). Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows. Modelling and Simulation in Engineering. Volume 2015, Article ID 591282, 11 pages. DOI: 10.1155/2015/591282
Rousseau, M., Cerdan, O., Delestre, O., Dupros, F., James, F., and Cordier, S. (2015). Overland Flow Modeling with the Shallow Water Equations Using a Well-Balanced Numerical Scheme: Better Predictions or Just More Complexity. Journal of Hydrologic Engineering , 20(10): ???. DOI: 10.1061/(ASCE)HE.1943-5584.0001171
Sætra M. L., Brodtkorb A. R., Lie K.-A. (2015). Efficient GPU-Implementation of Adaptive Mesh Refinement for the Shallow-Water Equations. Journal of Scientific Computing, 63(1) : 23-48. DOI: 10.1007/s10915-014-9883-4.
Wang L., Pan C. (2015). An analysis of dam-break flow on slope. Journal of Hydrodynamics, Ser. B. 26(6):902-911. DOI: 10.1016/S1001-6058(14)60099-8.
Zhang Y., Lin P. (2015) An improved SWE model for simulation of dam-break flows. Proceedings of the Institution of Civil Engineers - Water Management. DOI: 10.1680/wama.15.00021
2014
Bacigaluppi P., Ricchiuto M., Bonneton P. (2014). Upwind Stabilized Finite Element Modelling of Non-hydrostatic Wave Breaking and Run-up. Research Report #8536. Project-Team BACCHUS. URL: http://hal.inria.fr/hal-00990002.
De Rosis A. (2014). A lattice Boltzmann-finite element model for two-dimensional luid-structure interaction problems involving shallow waters. Advances in Water Resources, 65: 18-24. DOI: 10.1016/j.advwatres.2014.01.003
Doyen D., Gunawan P. H. (2014). An Explicit Staggered Finite Volume Scheme for the Shallow Water Equations. Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer. Proceedings in Mathematics & Statistics Volume 77, pp 227-235. DOI: 10.1007/978-3-319-05684-5_21.
Duran A. (2014). Numerical simulation of depth-averaged flow models : a class of Finite Volume and discontinuous Galerkin approaches. PhD Thesis. Université Montpellier II, France. https://tel.archives-ouvertes.fr/tel-01109438
Pasquetti R., Guermond J.L., Popov B. (2014). Stabilized spectral element approximation of the Saint Venant system using the entropy viscosity technique. International Conference on Spectral and High Order Method (ICOSAHOM 2014), Salt Lake City, June 23-27. 8 p. http://math1.unice.fr/~rpas/publis/ico14.pdf
Sætra M. L. (2014). Shallow Water Simulations on Graphics Hardware. PhD Thesis, Faculty of Mathematics and Natural Sciences, University of Oslo. ISSN 1501-7710. http://urn.nb.no/URN:NBN:no-45020
Yoshioka H., Unami K., Fujihara M. (2014). Friction slope formulae for the two-dimensional shallow water model. Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering), 70(4): I_55-I_60. (in Japanese) DOI: http://doi.org/10.2208/jscejhe.70.I_55
Yoshioka H., Unami K., Fujihara M. (2014). A Simple Finite Volume Model for Dam Break Problems in Multiply Connected Open Channel Networks with General Cross-Sections. Theoretical and Applied Mechanics Japan. 62: 131-140. DOI: 10.11345/nctam.62.131.
Yoshioka H., Unami K. & Fujihara M. (2014). A finite element/volume method model of the depth-averaged horizontally 2D shallow water equations. International Journal For Numerical Methods in Fluids, 75(1): 23-41. DOI: http://dx.doi.org/10.1002/fld.3882
2013
Cordier S., Coullon H., Delestre O., Laguerre C., Le M. H., Pierre D., Sadaka G. (2013). FullSWOF_Paral: Comparison of two parallelizations strategies (MPI and SkelGIS) on a software designed for hydrology applications. ESAIM: Proceedings. Vol. 43, p. 59-79. http://www.esaim-proc.org/articles/proc/pdf/2013/05/proc134304.pdf
Couderc F., Madec R., Monnier J., Vila J.-P. (2013). DassFow-Shallow, variational data assimilation for shallow-water models: Numerical schemes, user and developer Guides. Research Report, University of Toulouse, CNRS, IMT, INSA, ANR. https://hal.archives-ouvertes.fr/hal-01120285/
Yoshioka H., Unami K., Fujihara M. (2013). A highly efficient shallow water model based on a selective lumping algorithm. Annual meeting of the Japanese Society of Irrigation, Drainage and Reclamation Engineering. #4-15, p. 398-399. (in Japanese) http://soil.en.a.u-tokyo.ac.jp/jsidre/search/PDFs/13/13004-15.pdf
Yoshioka H., Unami K., Fujihara M. (2013). Hyperbolic dual finite volume models for shallow water flows in multiply-connected open channel networks. The 27th Computational Fluid Dynamics Symposium. Paper No. B07-01. http://www2.nagare.or.jp/cfd/cfd27/webproc/B07-1.pdf
Zhou F., Chen G.X., Huang Y.F., Yang J.Z. & Feng H. (2013). An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography. Water Resources Research, 49(4): 1914-1928. DOI: http://dx.doi.org/10.1002/wrcr.20179
2012
Berthon C., Foucher F. (2012). Efficient well-balanced hydrostatic upwind schemes for shallow-water equations, Journal of Computational Physics, 231(15): 4993-5015. DOI: 10.1016/j.jcp.2012.02.031.
Nguyen T. D. (2012). Impact de la résolution et de la précision de la topographie sur la modélisation de la dynamique d’invasion d’une crue en plaine inondable. PhD thesis. Univ. Toulouse, France. (in French) http://ethesis.inp-toulouse.fr/archive/00002210/01/nguyen.pdf
