SWASHES

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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: rf.s1529946767naelr1529946767o-vin1529946767u.set1529946767sil@t1529946767catno1529946767c.seh1529946767saws1529946767 (F. Darboux, O. Delestre, C. Laguerre, C. Lucas).

If you are using the Conda package manager, the SWASHES package is available at anaconda.org/lrntct/swashes. It works for linux 64 bits, windows 32 bits and windows 64 bits.
SWASHES is also available as a Python library named pyswashes. With it you can obtain the selected analytic solution in the form of a csv, Pandas dataframe, NumPy array or ASCII Grid format. See pyswashes.readthedocs.io/en/latest/.
The Conda package and the Python library have been developed by L. Courty.

How to cite: bibtex file
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

If you want to be informed of the main evolutions of SWASHES, please subscribe our newsletter http://listes.univ-orleans.fr/sympa/subscribe/swashes.infos.

Examples Bibliography Citations

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
http://hal.archives-ouvertes.fr/hal-00628246
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
http://hal.archives-ouvertes.fr/hal-00694195

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
http://hal.archives-ouvertes.fr/hal-00648343

Finally, SWASHES has been cited in:

  1. 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
  2. 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
  3. 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
  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
  5. Shallow Water Simulations on Graphics Hardware,
    Sætra M. L.,
    PhD Thesis, Faculty of Mathematics and Natural Sciences, University of Oslo, ISSN 1501-7710, 2014, http://urn.nb.no/URN:NBN:no-45020
  6. 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, http://hal.inria.fr/hal-00990002
  7. 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
  8. 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
  9. 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
  10. 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
  11. Gerris tests,
    Popinet J.,
    2013, http://gerris.dalembert.upmc.fr/gerris/tests/tests/index.html
  12. 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
  13. 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 https://hal.archives-ouvertes.fr/hal-01120285/
  14. 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
  15. 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/j.jcp.2012.02.031
  16. Solving Shallow Water flows in 2D with FreeFem++ on structured mesh,
    Sadaka G.,
    Research report, LAMFA, 2012, http://hal.archives-ouvertes.fr/hal-00715301
  17. 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
  18. 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, http://math1.unice.fr/~rpas/publis/ico14.pdf
  19. 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
  20. 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
  21. 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
  22. 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, http://congress.cimne.com/panacm2015/admin/files/fileabstract/a274.pdf
  23. 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), http://soil.en.a.u-tokyo.ac.jp/jsidre/search/PDFs/13/13004-15.pdf
  24. 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
  25. ANUGA Software: Open Source Hydrodynamic / Hydraulic Modelling Project,
    Australian National University and Geoscience Australia
    2015, http://github.com/GeoscienceAustralia/anuga_core/tree/master/validation_tests/analytical_exact
  26. 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) http://ethesis.inp-toulouse.fr/archive/00002210/01/nguyen.pdf
  27. Benchmarks of the Basilisk software,
    Kirstetter G.
    2013, http://basilisk.fr/sandbox/geoffroy/friction/README
  28. Software Framework for Solving Hyperbolic Conservation Laws Using OpenCL,
    Markussen J. K. R.
    Master thesis. Institutt for informatikk, University of Oslo, 2015. https://www.duo.uio.no/bitstream/handle/10852/44764/markussen-master.pdf?sequence=1&isAllowed=y
  29. 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, http://89.31.100.18/~iahrpapers/84826.pdf
  30. 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, https://tel.archives-ouvertes.fr/tel-01109438
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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, https://repositorium.sdum.uminho.pt/bitstream/1822/36932/1/Symcomp-jorge.pdf
  36. 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
  37. 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, http://www2.nagare.or.jp/cfd/cfd27/webproc/B07-1.pdf
  38. 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, http://www.opentelemac.org/downloads/Papers%20and%20Proceedings/telemac-mascaret_user_conference_2014-proceedings.pdf
  39. 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, http://www.esaim-proc.org/articles/proc/pdf/2015/01/proc144818.pdf
  40. 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
  41. A shallow water code,
    Chabot S.
    Internship Report, 2015, https://etu.chabotsi.fr/en-vrac/sw-report.pdf
  42. 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
  43. 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
  44. 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
  45. Simulation of Rain-Induced Floods on High Performance Computers Simulation,
    Scharoth N.
    Master’s Thesis in Informatics. Fakultät für Informatik. Technische Universität München, 2015 http://www5.in.tum.de/pub/Schaffroth2015_MasterThesis.pdf
  46. 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
  47. 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/j.jcp.2017.01.009
  48. 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. https://tel.archives-ouvertes.fr/tel-01288217/
  49. A hybrid finite-volume finite-difference rotational Boussinesq-type model of surf-zone hydrodynamics.
    Tatlock, B.
    PhD thesis, University of Nottingham, Nottingham, UK. 2015. http://eprints.nottingham.ac.uk/30443/
  50. 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
  51. 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
  52. 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
  53. 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
  54. 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. https://arxiv.org/abs/1607.04547
  55. A viscous layer model for a shallow water free surface flow.
    James F., Lagrée P.-Y., Legrand M.
    Preprint, 2016. https://hal.archives-ouvertes.fr/hal-01341563
  56. 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. http://mt.aics.riken.jp/publications/wahib_SC2016.pdf
  57. Numerical simulation of shallow water equations and related models.
    Gunawan H.P.
    PhD thesis, Université Paris-Est, France. 2015, https://hal.archives-ouvertes.fr/tel-01216642
  58. 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
  59. A GRASS GIS module for 2D superficial flow simulations.
    Courty L. G., Pedrozo-Acuña A.
    12th International Conference on Hydroinformatics, HIC 2016. https://zenodo.org/record/159617/files/Courty%20and%20Acu%C3%B1a%20-%20A%20GRASS%20GIS%20module%20for%202D%20superficial%20flow%20simulations.pdf
  60. Modélisation de problèmes de mécanique des fluides : approches théoriques et numériques.
    Lucas C.
    HDR. Univ. Orléans, France, 2016. https://hal.archives-ouvertes.fr/tel-01420101
  61. Development of high-order well-balanced schemes for geophysical flows.
    Michel-Dansac V.
    PhD thesis, Univ. Nantes, France, 2016. https://hal.archives-ouvertes.fr/tel-01384958
  62. 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
  63. Discrete Boltzmann model of shallow water equations with polynomial equilibria.
    Meng J., Gu X.-J., Emerson D. R., Peng Y., Zhang J.
    Preprint, 2016. https://arxiv.org/abs/1609.03735
  64. 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
  65. Nouveaux schémas de convection pour les écoulements à surface libre
    Pavan S.
    PhD thesis, Univ. Paris-Est, France, 2016. http://www.theses.fr/2016PESC1011
  66. 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
  67. 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. https://www.researchgate.net/publication/310607583_Simulacao_de_onda_de_mare_por_meio_do_Metodo_do_Reticulado_de_Boltzmann
  68. 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/j.jcp.2016.11.032
  69. 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
  70. 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. http://hdl.handle.net/2152/41984
  71. 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/j.jcp.2016.12.030
  72. 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
  73. 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
  74. 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. https://hal.archives-ouvertes.fr/tel-01430609
  75. 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
  76. 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
  77. 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
  78. Coupling methods for 2D/1D shallow water flow models for flood simulations.
    Nwaigwe C.
    PhD thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/id/eprint/88277
  79. 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
  80. Etude mathématique de modèles de couches visqueuses pour des écoulements naturels.
    Legrand M.
    PhD Thesis, Univ. d’Orléans, 2016. https://tel.archives-ouvertes.fr/tel-01529756/
  81. 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. https://www.researchgate.net/publication/318429066_MUSCL_vs_MOOD_Techniques_to_Solve_the_SWE_in_the_Framework_of_Tsunami_Events
  82. Numerical simulations of hydraulic jumps with the Shear Shallow Water model.
    Delis A., Guillard H., Tai. Y.-C.
    Research Report RR-9127, INRIA Sophia Antipolis – Méditerranée; UCA, Inria. 2017. https://hal.inria.fr/hal-01647019/

  83. GPU driven finite difference WENO scheme for real time solution of the shallow water equations.
    Parna P., Meyer K., Falconer R.
    Computers & Fluids. 161: 107-120, 2018. doi : 10.1016/j.compfluid.2017.11.012
  84. Well-balanced discontinuous Galerkin method and finite volume WENO scheme based on hydrostatic reconstruction for blood flow model in arteries.
    Li G., Delestre O., Yuan L.
    Numerical methods in fluids. 86(7) : 491-508, 2017. doi : 10.1002/fld.4463
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    Willams D. H.
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