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SWASHES: Shallow Water Analytic Solutions for Hydraulic and Environmental Studies.

SWASHES is a library of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies.
A significant number of analytic solutions to the Shallow Water equations is described in a unified formalism. They encompass a wide variety of flow conditions (supercritical, subcritical, shock, etc.), in 1 or 2 space dimensions, with or without rain and soil friction, for transitory flow or steady state.
The goal of this code is to help users of Shallow Water based models to easily find an adaptable benchmark library to validate numerical methods.

The SWASHES software can be downloaded on the website sourcesup.
This software is distributed under CeCILL-V2 (GPL compatible) free software license. So, you are authorized to use the Software, without any limitation as to its fields of application.
For any question, contact us at: (F. Darboux, O. Delestre, C. Laguerre, C. Lucas).

If you want to be informed of the main evolutions of SWASHES, please subscribe our newsletter


Some examples (used in comparison with FullSWOF approximate solutions):

Transcritical flow with shock
Mac Donald's type solution with a smooth transition and a shock
Dam break on a dry domain without friction
Thacker's planar surface in a paraboloid
Mac Donald pseudo-2D supercritical solution
MacDonald pseudo-2d subcritical solution

For more details we refer to the documentation of the code.

You can also read the following articles:

SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies,
  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
  Errata: International Journal for Numerical Methods in Fluids, 74(3): 229-230, 2014, doi:10.1002/fld.3865
  - in equation (4), read A(W) = F'(W) = (0   1 \\ -u2+gh   2u),
  - in equation (10),
   * in the first line, xshock must be replaced by x, for x < xshock;
   * in the second line, xshock must be replaced by x, for x > xshock;
   * h1 = h(xshock-), h2= h(xshock+).
  - in paragraph 4.1.1, the value of cm is solution of - 8ghr cm2 (ghl - cm)2+(cm2- ghr)2(cm2+ghr)=0.,
  - in paragraphs 4.1.1, 4.1.2 and 4.1.3, in the expressions of h, u, α1 and α2, x must be replaced by x-x0.

SWASHES: A library for benchmarking in hydraulics,
  O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, F. James, S. Cordier,
  Advances in Hydroinformatics - SIMHYDRO 2012 - New Frontiers of Simulation, P. Gourbesville, J. Cunge, and G. Caignaert (Ed.), 233-243, 2014, doi:10.1007/978-981-4451-42-0_20

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

Finally, SWASHES has been cited in:

A non-hydrostatic model for water waves in nearshore region,
 Fang K., Sun J., Liu Z., Yin J.,
 Advances in Water Science, 26(1): 114-122, 2015, (in Chinese), doi: 10.14042/j.cnki.32.1309.2015.01.015

An analysis of dam-break flow on slope,
 Wang L., Pan C.,
 Journal of Hydrodynamics, Ser. B. 26(6):902-911, 2015, doi: 10.1016/S1001-6058(14)60099-8

Efficient GPU-Implementation of Adaptive Mesh Refinement for the Shallow-Water Equations,
 Sætra M. L., Brodtkorb A. R., Lie K.-A.,
 Journal of Scientific Computing, 63(1): 23-48, 2015, doi: 10.1007/s10915-014-9883-4

The MOOD method for the non-conservative shallow-water system,
 Clain S., Figueiredo J.,
 Computers & Fluids, 145, 99–128, 2017 doi: 10.1016/j.compfluid.2016.11.013

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

Upwind Stabilized Finite Element Modelling of Non-hydrostatic Wave Breaking and Run-up,
 Bacigaluppi P., Ricchiuto M., Bonneton P.,
 Research Report #8536, Project-Team BACCHUS, 2014,

An Explicit Staggered Finite Volume Scheme for the Shallow Water Equations. Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects,
 Doyen D., Gunawan P. H.,
 Springer Proceedings in Mathematics & Statistics, 77: 227-235, 2014, doi: 10.1007/978-3-319-05684-5_21

A Simple Finite Volume Model for Dam Break Problems in Multiply Connected Open Channel Networks with General Cross-Sections,
 Yoshioka H., Unami K., Fujihara M.,
 Theoretical and Applied Mechanics Japan, 62: 131-140, 2014, doi: 10.11345/nctam.62.131

A finite element/volume method model of the depth-averaged horizontally 2D shallow water equations,
  Yoshioka H., Unami K., Fujihara M.,
  International Journal For Numerical Methods in Fluids, 75(1): 23-41, 2014, doi: 10.1002/fld.3882

A lattice Boltzmann-finite element model for two-dimensional fluid-structure interaction problems involving shallow waters,
 De Rosis A.,
 Advances in Water Resources, 65: 18-24, 2014, doi: 10.1016/j.advwatres.2014.01.003

Gerris tests,
 Popinet J.,

FullSWOF_Paral: Comparison of two parallelizations strategies (MPI and SkelGIS) on a software designed for hydrology applications,
 Cordier S., Coullon H., Delestre O., Laguerre C., Le M. H., Pierre D., Sadaka G,
 ESAIM Proceedings, 43: 59-79, 2013, doi:10.1051/proc/201343004

DassFow-Shallow, variational data assimilation for shallow-water models: Numerical schemes, user and developer Guides,
 Couderc F., Madec R., Monnier J., Vila J.-P.
 Research Report, University of Toulouse, CNRS, IMT, INSA, ANR, 2013

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography,
 Zhou F., Chen G.X., Huang Y.F., Yang J.Z., Feng H.,
 Water Resources Research, 49(4): 1914-1928, 2013, doi: 10.1002/wrcr.20179

Efficient well-balanced hydrostatic upwind schemes for shallow-water equations,
 Berthon C., Foucher F.,
 Journal of Computational Physics, 231(15): 4993-5015, 2012, doi: 10.1016/

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

A faster numerical scheme for a coupled system modeling soil erosion and sediment transport,
 Le M.-H., Cordier S., Lucas C., Cerdan O.,
 Water Resources Research, 51(2): 987-1005, 2015, doi: 10.1002/2014WR015690

Stabilized spectral element approximation of the Saint Venant system using the entropy viscosity technique,
 Pasquetti R., Guermond J.L., Popov B.
 International Conference on Spectral and High Order Method (ICOSAHOM 2014), Salt Lake City, June 23-27, 8 p., 2014,

Consistent Weighted Average Flux of Well-balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows,
 Pongsanguansin T., Maleewong M., Mekchay K.
 Modelling and Simulation in Engineering, Article ID 591282, 2015, doi 10.1155/2015/591282

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

Second Order Discontinuous Galerkin scheme for compound natural channels with movable bed. Applications for the computation of rating curves,
 Minatti L., De Cicco P. N., Solari L.
 Advances in Water Resources, In Press, 2015, doi 10.1016/j.advwatres.2015.06.007

Solution of two-dimensional Shallow Water Equations by a localized Radial Basis Function collocation method,
 Bustamante C. A. , Power H., Nieto C., Florez W. F.
 1st Pan-American Congress on Computational Mechanics. International Association for Computational Mechanics. Buenos Aires, April 27-29, 2015,

A highly efficient shallow water model based on a selective lumping algorithm,
 Yoshioka H., Unami K., Fujihara M.
 Annual meeting of the Japanese Society of Irrigation, Drainage and Reclamation Engineering., 4-15: 398-399, 2013, (in Japanese),

Friction slope formulae for the two-dimensional shallow water model,
 Yoshioka H., Unami K., Fujihara M.
 Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering), 70(4): I_55-I_60, 2014, (in Japanese), doi 10.2208/jscejhe.70.I_55

ANUGA Software: Open Source Hydrodynamic / Hydraulic Modelling Project,
 Australian National University and Geoscience Australia

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,
 Nguyen T. D.
 PhD thesis. Univ. Toulouse, France, 2012, (in French)

Benchmarks of the Basilisk software,
 Kirstetter G.

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

High resolution rainfall-runoff simulation in urban aera: Assessment of Telemac-2D and FullSWOF-2D,
 Ma Q., Abily M., Vo. N. D., Gourbesville P.
 E-proceedings of the 36th IAHR World Congress, The Hague, the Netherlands, 28 June - 3 July, 2015,

Numerical simulation of depth-averaged flow models : a class of Finite Volume and discontinuous Galerkin approaches,
 Duran A.
 PhD Thesis, Univ. Montpellier II, France, 2014,

Comparison and Validation of Two Parallelization Approaches of FullSWOF_2D Software on a Real Case. Advances in Hydroinformatics,
 Delestre O., Abily M., Cordier F., Gourbesville P., Coullon H.
 Advances in Hydroinformatics. Simhydro 2014. Part 2, pp. 395-407, 2016, doi 10.1007/978-981-287-615-7_27

Numerical Scheme for a Viscous Shallow Water System Including New Friction Laws of Second Order: Validation and Application,
 Delestre O., Razafison U.
 Advances in Hydroinformatics. Simhydro 2014. Part 1, pp. 227-239, 2016, doi 10.1007/978-981-287-615-7_16

An improved SWE model for simulation of dam-break flows,
 Zhang Y., Lin P.
 Proceedings of the Institution of Civil Engineers - Water Management, 2015, doi 10.1680/wama.15.00021

Hydrostatic relaxation scheme for the 1D shallow water - Exner equations in bedload transport,
 Gunawan P. H., Lhébrard X.
 Computers & Fluids, 121: 44-50, 2015, doi 10.1016/j.compfluid.2015.08.001

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

Overland Flow Modeling with the Shallow Water Equations Using a Well-Balanced Numerical Scheme: Better Predictions or Just More Complexity,
 Rousseau, M., Cerdan, O., Delestre, O., Dupros, F., James, F., and Cordier, S.
 Journal of Hydrologic Engineering , 20(10), 2015, doi 10.1061/(ASCE)HE.1943-5584.0001171

Hyperbolic dual finite volume models for shallow water flows in multiply-connected open channel networks,
 Yoshioka H., Unami K., Fujihara M.
 The 27th Computational Fluid Dynamics Symposium, Paper No. B07-01, 2013,

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

Uncertainty related to high resolution topographic data use for flood event modeling over urban areas: Toward a sensitivity analysis approach,
 Abily M., Delestre O., Amossé L., Bertrand N., Richet Y., Duluc C.-M., Gourbesville P., Navaro P.
 In, N. Champagnat, T. Lelièvre, A. Nouy (Eds), ESAIM Proceedings and Surveys, 48: 385-399, 2015,

A well-balanced FV scheme for compound channels with complex geometry and movable bed,
 Minatti L.
 Water Resources Research, 51(8):6564-6585, 2015, doi 10.1002/2014WR016584

A shallow water code,
 Chabot S.
 Internship Report, 2015,

Numerical comparison of shallow water models in multiply connected open channel networks,
 Yoshioka H., Unami K. and Fujihara M.
 Journal of Advanced Simulation in Science and Engineering, 2(2): 271-291, 2015, doi 10.15748/jasse.2.271

Free Surface Axially Symmetric Flows and Radial Hydraulic Jumps,
 Valiani, A. and Caleffi, V.
 J. Hydraul. Eng., 2015 doi 10.1061/(ASCE)HY.1943-7900.0001104

Hydrokinetic turbine location analysis by a local collocation method with radial basis functions for two-dimensional shallow water equations,
 Bustamante C. A., Florez W. F., Power H. and Hill A. F.
 WIT Transactions on Ecology and the Environment, 195:11, 2015 doi 10.2495/ESUS150011

Simulation of Rain-Induced Floods on High Performance Computers Simulation,
 Scharoth N.
 Master's Thesis in Informatics. Fakultät für Informatik. Technische Universität München, 2015

The Tagus 1969 tsunami simulation with a finite volume solver and the hydrostatic reconstruction technique,
  Clain S., Reis C., Costa R., Figueiredo J., Baptista M. A., Miranda J. M.
  Preprint, 2015, hal-01239498

A well-balanced scheme for the shallow-water equations with topography or Manning friction,
 Michel-Dansac V., Berthon C., Clain S., Foucher F.
  Journal of Computational Physics, 335, 115–154, 2017. doi: 10.1016/

High-resolution modelling with bi-dimensional shallow water equations based codes : high-resolution topographic data use for flood hazard assessment over urban and industrial environments.
  Abily M.
  PhD thesis, Université Nice Sophia Antipolis, France. 2015.

A hybrid finite-volume finite-difference rotational Boussinesq-type model of surf-zone hydrodynamics.
  Tatlock, B.
  PhD thesis, University of Nottingham, Nottingham, UK. 2015.

Well-balanced finite difference weighted essentially non-oscillatory schemes for the blood flow model.
  Wang Z., Li G., Delestre, O.
  International Journal for Numerical Methods in Fluids, 2016. doi:10.1002/fld.4232

Parallelization of a relaxation scheme modelling the bedload transport of sediments in shallow water flow.
  Audusse E., Delestre O., Le M.H., Masson-Fauchier M., Navaro P., Serra R.
  ESAIM Proceedings, 43: 80-94, 2013. doi:10.1051/proc/201343005

On the Convergence of a Shock Capturing Discontinuous Galerkin Method for Nonlinear Hyperbolic Systems of Conservation Laws.
  Zakerzadeh M., May G.
  SIAM J. Numer. Anal., 54(2), 874–898, 2016. doi: 10.1137/14096503X

Meshless particle modelling of free surface flow over spillways.
  Jafari-Nadoushan E., Hosseini K., Shakibaeinia A., Mousavi S.-F.
  Journal of Hydroinformatics, 18(2), 354-370, 2016. doi: 10.2166/hydro.2015.096

A continuous/discontinuous Galerkin solution of the shallow water equations with dynamic viscosity, high-order wetting and drying, and implicit time integration.
  Marras S., Kopera M.A., Constantinescu E. M., Suckale J., Giraldo F. X.
  Preprint, 2016.

A viscous layer model for a shallow water free surface flow.
  James F., Lagrée P.-Y., Legrand M.
  Preprint, 2016.

Daino: A High-level Framework for Parallel and Efficient AMR on GPUs.
  Wahib M., Maruyama N., Aoki T.
  SC16: The International Conference for High Performance Computing, Networking, Storage and Analysis 2016, Salt Lake City, UT, USA; November 2016.

Numerical simulation of shallow water equations and related models.
  Gunawan H.P.
  PhD thesis, Université Paris-Est, France. 2015.

A Newton multigrid method for steady-state shallow water equations with topography and dry areas.
  Wu K., Tang H.
  Applied Mathematics and Mechanics, 37(11), 1441–1466, 2016. doi: 10.1007/s10483-016-2108-6
A GRASS GIS module for 2D superficial flow simulations.
  Courty L. G., Pedrozo-Acuña A.
  12th International Conference on Hydroinformatics, HIC 2016.

Modélisation de problèmes de mécanique des fluides : approches théoriques et numériques.
  Lucas C.
  HDR. Univ. Orléans, France, 2016.

Development of high-order well-balanced schemes for geophysical flows.
  Michel-Dansac V.
  PhD thesis, Univ. Nantes, France, 2016.

Shallow water equations: Split-form, entropy stable, well-balanced, and positivity preserving numerical methods.
  Ranocha H.
  International Journal on Geomathematics, 8(1), 85-133, 2017. doi: 10.1007/s13137-016-0089-9

Discrete Boltzmann model of shallow water equations with polynomial equilibria.
  Meng J., Gu X.-J., Emerson D. R., Peng Y., Zhang J.
  Preprint, 2016.

Itzï (version 17.1): an open-source, distributed GIS model for dynamic flood simulation.
  Courty L. G., Pedrozo-Acuña A., Bates P. D.
  Geosci. Model Dev., 10, 1835-1847, 2017. doi: 10.5194/gmd-10-1835-2017

Nouveaux schémas de convection pour les écoulements à surface libre
  Pavan S.
  PhD thesis, Univ. Paris-Est, France, 2016.

Shallow-water simulations by a well-balanced WAF finite volume method: a case study to the great flood in 2011, Thailand
  Pongsanguansin T., Maleewong M., Mekchay K.
  Computational Geosciences, 20(6), 1269–1285, 2016. doi: 10.1007/s10596-016-9589-9

Simulação de onda de maré por meio do Método do Reticulado de Boltzmann.
  Galina V., Cargnelutti J., Kaviski E., Gramani L. M., Lobeiro A. M.
  Conference: I Simpósio de Métodos Numéricos em Engenharia, At Curitiba, 2016.

Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties
  Ghigo A. R., Delestre O., Fullana J.-M., Lagrée P.-Y.
  Journal of Computational Physics, 331, 108-136, 2017. doi: 10.1016/

Second-order finite volume with hydrostatic reconstruction for tsunami simulation.
  Clain S., Reis C., Costa R., Figueiredo J., Baptista M. A., Miranda J. M.
  J. Adv. Model. Earth Syst., 2016. doi: 10.1002/2015MS000603

Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds.
  Neupane P.
  PhD thesis. Univ. Texas Austin, USA, 2016.

Three-dimensional shallow water system: A relaxation approach.
  Liu X., Mohammadian A., Infante Sedano J. Á., Kurganov A.
  Journal of Computational Physics, 333, 160 - 179, 2017. doi: 10.1016/

A central moments-based lattice Boltzmann scheme for shallow water equations
  De Rosis A.
  Computer Methods in Applied Mechanics and Engineering, 319, 379–392, 2017. doi: 10.1016/j.cma.2017.03.001

Simulation of Free-Surface Flow Using the Smoothed Particle Hydrodynamics (SPH) Method with Radiation Open Boundary Conditions.
  Ni X., Sheng J., Feng W.
  Journal of Atmospheric and Oceanic Technology, 33(11), 2435–2460, 2016. doi: 10.1175/JTECH-D-15-0179.1

Free surface flow simulation in estuarine and coastal environments : numerical development and application on unstructured meshes.
  Filippini, A.G.
  PhD Thesis, Univ. de Bordeaux, 2016.

A new finite volume approach for transport models and related applications with balancing source terms.
  Abreu E., Lambert W., Perez J., Santo A.
  Mathematics and Computers in Simulation, 137, 2-28, 2017. doi: 10.1016/j.matcom.2016.12.012

High-order discontinuous Galerkin methods with Lagrange multiplier for hyperbolic systems of conservation laws.
  Kim M.-Y., Park E.-J., Shin, J.
  Computers and Mathematics with Applications, 73(9), 1945-1974, 2017. doi: 10.1016/j.camwa.2017.02.039

A mass conservative well-balanced reconstruction at wet/dry interfaces for the Godunov-type shallow water model.
  Fiser M., Ozgen I., Hinkelmann R., Vimmr J.
  International Journal for Numerical Methods in Fluids, 82(12), 893-908, 2016. doi: 10.1002/fld.4246

Coupling methods for 2D/1D shallow water flow models for flood simulations.
  Nwaigwe C.
  PhD thesis, University of Warwick, 2016.

A Godunov-Type Scheme for Shallow Water Equations Dedicated to Simulations of Overland Flows on Stepped Slopes.
  Goutal N., Le M.-H., Ung P.
  International Conference on Finite Volumes for Complex Applications, FVCA 2017: Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, p 275-283, 2017. doi: 10.1007/978-3-319-57394-6_30

Etude mathématique de modèles de couches visqueuses pour des écoulements naturels.
  Legrand M.
  PhD Thesis, Univ. d'Orléans, 2016.

MUSCL vs MOOD Techniques to Solve the SWE in the Framework of Tsunami Events.
  Reis C., Figueiredo J., Clain S., Omira R., Baptista M.A., Miranda J.
  SYMCOMP 2017 Guimarães, 6-7 April 2017, ECCOMAS, Portugal, p. 189-213, 2017.