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24, chemin de Borde Rouge -Auzeville - CS52627 31326 Castanet Tolosan cedex - France

Last update: May 2021

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Soil Science Research Unit


The SWASHES software

« 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

h-McDo-100-fluv-Man © INRA

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


h-dam-dry © INRA

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


h-Thacker-2D-plan © INRA

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

To be informed of the changes in SWASHES, subscribe to the diffusion list

Distribution:Free source code, in English.

Documentation: Manuals of SWASHES

O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, T. N. T. Vo, F. James, S. Cordier,  International Journal for Numerical Methods in Fluids, 72(3): 269-300, 2013, doi:10.1002/fld.3741


  1. in equation (4), readA(W) = F'(W) = (0   1 \\ -u^2+gh   2u),      
  2. in sections  4.1.1, 4.1.2 et 4.1.3, in the expressions ofh, u, alpha_1, alpha_2, xhave to be replaced by parx-x_0.


Download: from SourceSup


Contact: Frédéric DARBOUX


See also:

FullSWOF, a code solving shallow-water equations, and validated using SWASHES.

GARS, a generator of rough surfaces.


O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, T. N. T. Vo, F. James, S. Cordier, SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies, International Journal for Numerical Methods in Fluids, 72(3): 269-300, 2013, doi:10.1002/fld.3741

C. Berthon, S. Cordier, O. Delestre, M. H. Le, An analytical solution of the shallow water system coupled to the Exner equation, C. R. Acad. Sci. Paris, Ser. I 350(3-4):183-186, 2012, doi:10.1016/j.crma.2012.01.007

Citations of SWASHES


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.

Australian National University and Geoscience Australia (2015). ANUGA Software: Open Source Hydrodynamic / Hydraulic Modelling Project.

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.

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

Figueiredo J. M., Clain S. (2015). Second-order finite volume mood method for the shallow water with dry/wet interface. SYMCOMP 2015 - ECCOMAS, March 26-27, Faro, Portugal.

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:

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.

Markussen J. K. R. (2015). Software Framework for Solving Hyperbolic Conservation Laws Using OpenCL. Master thesis. Institutt for informatikk, University of Oslo.

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:

Neupane P., Dawson C. (2015). A discontinuous Galerkin method for modeling flow in networks of channels. Advances in Water Resources, 79: 61-79. DOI: 10.1016/j.advwatres.2015.02.012.

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


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:

Clain S., Figueiredo J. (2014). The MOOD method for the non-conservative shallow-water system. Submitted preprint. URL:

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.

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.

Sætra M. L. (2014). Shallow Water Simulations on Graphics Hardware. PhD Thesis, Faculty of Mathematics and Natural Sciences, University of Oslo. ISSN 1501-7710.

Stadler L., Brudy-Zippelius T. (2014). A study of the HLLC scheme of TELEMAC-2D. Proceedings of the 21st Telemac Mascaret user conference. 15-17 October. Grenoble, France. pp. 185-192.

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:

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:


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.

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.

Kirstetter G. (2013). Benchmarks of the Basilisk software.

Popinet J. (2013). Gerris tests.

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)

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.

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:


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/

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)

Sadaka G. (2012). Solving Shallow Water flows in 2D with FreeFem++ on structured mesh. Research report, LAMFA. URL: