A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
ESAIM: M2AN, 45 1 (2011) 169-200
Published online: 2010-06-24
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
How do microalgae perceive light in a high-rate pond? Towards more realistic Lagrangian experiments
David Demory, Charlotte Combe, Philipp Hartmann, et al.Royal Society Open Science 5 (5) 180523 (2018)
DOI: 10.1098/rsos.180523
See this article
Advances in Numerical Simulation in Physics and Engineering
Enrique D. Fernández-Nieto and Paul VigneauxSEMA SIMAI Springer Series, Advances in Numerical Simulation in Physics and Engineering 3 51 (2014)
DOI: 10.1007/978-3-319-02839-2_2
See this article
Global stability of weak solutions for a multilayer Saint–Venant model with interactions between layers
Bernard Di Martino, Boris Haspot and Yohan PenelNonlinear Analysis 163 177 (2017)
DOI: 10.1016/j.na.2017.07.010
See this article
Numerical simulations of a non-hydrostatic shallow water model
Marie-Odile Bristeau, Nicole Goutal and Jacques Sainte-MarieComputers & Fluids 47 (1) 51 (2011)
DOI: 10.1016/j.compfluid.2011.02.013
See this article
An efficient splitting technique for two-layer shallow-water model
Christophe Berthon, Françoise Foucher and Tomás MoralesNumerical Methods for Partial Differential Equations 31 (5) 1396 (2015)
DOI: 10.1002/num.21949
See this article
A 2D nonlinear multiring model for blood flow in large elastic arteries
Arthur R. Ghigo, Jose-Maria Fullana and Pierre-Yves LagréeJournal of Computational Physics 350 136 (2017)
DOI: 10.1016/j.jcp.2017.08.039
See this article
2D granular flows with the μ(I) rheology and side walls friction: A well-balanced multilayer discretization
E.D. Fernández-Nieto, J. Garres-Díaz, A. Mangeney and G. Narbona-ReinaJournal of Computational Physics 356 192 (2018)
DOI: 10.1016/j.jcp.2017.11.038
See this article
Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization
Luca Bonaventura, Enrique D. Fernández-Nieto, José Garres-Díaz and Gladys Narbona-ReinaJournal of Computational Physics 364 209 (2018)
DOI: 10.1016/j.jcp.2018.03.017
See this article
Granular front for flow down a rough incline: about the value of the shape factor in depths averaged models
Pierre-Yves Lagrée, Guillaume Saingier, Stéphanie Deboeuf, et al.EPJ Web of Conferences 140 03046 (2017)
DOI: 10.1051/epjconf/201714003046
See this article
Using the Multilayer Free-Surface Flow Model to Solve Wave Problems
V. A. Prokof’evPower Technology and Engineering 50 (5) 459 (2017)
DOI: 10.1007/s10749-017-0733-z
See this article
Studies on the Action of Waves on Maritime Hydraulic-Engineering Structures
A. A. Girgidov, V. I. Klimovich and V. A. Prokof’evPower Technology and Engineering 50 (5) 480 (2017)
DOI: 10.1007/s10749-017-0736-9
See this article
Stability and Boundary Stabilization of 1-D Hyperbolic Systems
Georges Bastin and Jean-Michel CoronProgress in Nonlinear Differential Equations and Their Applications, Stability and Boundary Stabilization of 1-D Hyperbolic Systems 88 1 (2016)
DOI: 10.1007/978-3-319-32062-5_1
See this article
A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution
E. D. Fernández-Nieto, E. H. Koné and T. Chacón RebolloJournal of Scientific Computing 60 (2) 408 (2014)
DOI: 10.1007/s10915-013-9802-0
See this article
A fast finite volume solver for multi-layered shallow water flows with mass exchange
Emmanuel Audusse, Fayssal Benkhaldoun, Saida Sari, Mohammed Seaid and Pablo TassiJournal of Computational Physics 272 23 (2014)
DOI: 10.1016/j.jcp.2014.04.026
See this article
A compressible two-layer model for transient gas–liquid flows in pipes
Charles Demay and Jean-Marc HérardContinuum Mechanics and Thermodynamics 29 (2) 385 (2017)
DOI: 10.1007/s00161-016-0531-0
See this article
A simple multi-layer finite volume solver for density-driven shallow water flows
Fayssal Benkhaldoun, Saida Sari and Mohammed SeaidMathematics and Computers in Simulation 99 170 (2014)
DOI: 10.1016/j.matcom.2013.04.016
See this article
A multilayer shallow model for dry granular flows with the -rheology: application to granular collapse on erodible beds
E. D. Fernández-Nieto, J. Garres-Díaz, A. Mangeney and G. Narbona-ReinaJournal of Fluid Mechanics 798 643 (2016)
DOI: 10.1017/jfm.2016.333
See this article
A multilayer shallow water system for polydisperse sedimentation
E.D. Fernández-Nieto, E.H. Koné, T. Morales de Luna and R. BürgerJournal of Computational Physics 238 281 (2013)
DOI: 10.1016/j.jcp.2012.12.008
See this article
A 2D model for hydrodynamics and biology coupling applied to algae growth simulations
Olivier Bernard, Anne-Céline Boulanger, Marie-Odile Bristeau and Jacques Sainte-MarieESAIM: Mathematical Modelling and Numerical Analysis 47 (5) 1387 (2013)
DOI: 10.1051/m2an/2013072
See this article
Approximation of the hydrostatic Navier–Stokes system for density stratified flows by a multilayer model: Kinetic interpretation and numerical solution
E. Audusse, M.-O. Bristeau, M. Pelanti and J. Sainte-MarieJournal of Computational Physics 230 (9) 3453 (2011)
DOI: 10.1016/j.jcp.2011.01.042
See this article
A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model
Eirik Holm Fyhn, Karl Yngve Lervåg, Åsmund Ervik and Øivind WilhelmsenPhysics of Fluids 31 (12) 122103 (2019)
DOI: 10.1063/1.5126168
See this article
Multilayer open flow model: A simple pressure correction method for wave problems
Vladimir ProkofevInternational Journal for Numerical Methods in Fluids 86 (8) 519 (2018)
DOI: 10.1002/fld.4465
See this article
The Linearized 2D Inviscid Shallow Water Equations in a Rectangle: Boundary Conditions and Well-Posedness
Aimin Huang and Roger TemamArchive for Rational Mechanics and Analysis 211 (3) 1027 (2014)
DOI: 10.1007/s00205-013-0702-0
See this article
A multilayer ice-flow model generalising the shallow shelf approximation
Guillaume JouvetJournal of Fluid Mechanics 764 26 (2015)
DOI: 10.1017/jfm.2014.689
See this article
Congested shallow water model: roof modeling in free surface flow
Edwige Godlewski, Martin Parisot, Jacques Sainte-Marie and Fabien WahlESAIM: Mathematical Modelling and Numerical Analysis 52 (5) 1679 (2018)
DOI: 10.1051/m2an/2018032
See this article
A well-posed multilayer model for granular avalanches with μ(I) rheology
L. Sarno, Y.-C. Tai, Y. Wang and M. OberlackPhysics of Fluids 33 (10) 103319 (2021)
DOI: 10.1063/5.0065697
See this article
Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system
Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau and Jacques Sainte-MarieMathematics of Computation 85 (302) 2815 (2016)
DOI: 10.1090/mcom/3099
See this article
On the modelling of shallow turbidity flows
Valery Yu. Liapidevskii, Denys Dutykh and Marguerite GisclonAdvances in Water Resources 113 310 (2018)
DOI: 10.1016/j.advwatres.2018.01.017
See this article
State Feedback Stabilization of the Linearized Bilayer Saint-Venant Model
Ababacar Diagne, Shuxia Tang, Mamadou Diagne and Miroslav KrsticIFAC-PapersOnLine 49 (8) 130 (2016)
DOI: 10.1016/j.ifacol.2016.07.431
See this article
Growth Rate Estimation of algae in Raceway Ponds: A novel Approach
Philipp Hartmann, David Demory, Charlotte Combe, et al.IFAC Proceedings Volumes 47 (3) 6216 (2014)
DOI: 10.3182/20140824-6-ZA-1003.02408
See this article
Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model
Shin-Jye Liang, Chih-Chieh Young, Chi Dai, Nan-Jing Wu and Tai-Wen HsuWater 12 (10) 2832 (2020)
DOI: 10.3390/w12102832
See this article
Beyond Shallow Water: Appraisal of a numerical approach to hydraulic jumps based upon the Boundary Layer theory
Francesco De Vita, Pierre-Yves Lagrée, Sergio Chibbaro and Stéphane PopinetEuropean Journal of Mechanics - B/Fluids 79 233 (2020)
DOI: 10.1016/j.euromechflu.2019.09.010
See this article
Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities
Nina Aguillon, Emmanuel Audusse, Edwige Godlewski and Martin ParisotSIAM Journal on Mathematical Analysis 50 (5) 4861 (2018)
DOI: 10.1137/17M1152887
See this article
A Multilayer Shallow Water Approach for Polydisperse Sedimentation with Sediment Compressibility and Mixture Viscosity
Raimund Bürger, Enrique D. Fernández-Nieto and Víctor OsoresJournal of Scientific Computing 85 (2) (2020)
DOI: 10.1007/s10915-020-01334-6
See this article
Well-balanced and shock-capturing solving of 3D shallow-water equations involving rapid wetting and drying with a local 2D transition approach
Xinhua Lu, Bing Mao, Xiaofeng Zhang and Shi RenComputer Methods in Applied Mechanics and Engineering 364 112897 (2020)
DOI: 10.1016/j.cma.2020.112897
See this article
An Efficient Two-Layer Non-hydrostatic Approach for Dispersive Water Waves
C. Escalante, E. D. Fernández-Nieto, T. Morales de Luna and M. J. CastroJournal of Scientific Computing 79 (1) 273 (2019)
DOI: 10.1007/s10915-018-0849-9
See this article
Derivation of a Multilayer Approach to Model Suspended Sediment Transport: Application to Hyperpycnal and Hypopycnal Plumes
T. Morales de Luna, E.D. Fernández Nieto and M. J. Castro DíazCommunications in Computational Physics 22 (5) 1439 (2017)
DOI: 10.4208/cicp.OA-2016-0215
See this article
118 627 (2021)
DOI: 10.1007/978-1-0716-1344-3_7
See this article
Modeling shallow water waves
D LannesNonlinearity 33 (5) R1 (2020)
DOI: 10.1088/1361-6544/ab6c7c
See this article
Towards a new friction model for shallow water equations through an interactive viscous layer
François James, Pierre-Yves Lagrée, Minh H. Le and Mathilde LegrandESAIM: Mathematical Modelling and Numerical Analysis 53 (1) 269 (2019)
DOI: 10.1051/m2an/2018076
See this article
A dynamic multilayer shallow water model for polydisperse sedimentation
Raimund Bürger, Enrique D. Fernández-Nieto and Víctor OsoresESAIM: Mathematical Modelling and Numerical Analysis 53 (4) 1391 (2019)
DOI: 10.1051/m2an/2019032
See this article
Numerical approximation of the 3D hydrostatic Navier–Stokes system with free surface
Sebastien Allgeyer, Marie-Odile Bristeau, David Froger, et al.ESAIM: Mathematical Modelling and Numerical Analysis 53 (6) 1981 (2019)
DOI: 10.1051/m2an/2019044
See this article
A Second-Order Well-Balanced Finite Volume Scheme for the Multilayer Shallow Water Model with Variable Density
Ernesto Guerrero Fernández, Manuel Jesús Castro-Díaz and Tomás Morales de LunaMathematics 8 (5) 848 (2020)
DOI: 10.3390/math8050848
See this article
A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows
Stéphane PopinetJournal of Computational Physics 418 109609 (2020)
DOI: 10.1016/j.jcp.2020.109609
See this article
A combined fluid-dynamic and thermodynamic model to predict the onset of rapid phase transitions in LNG spills
Karl Yngve Lervåg, Hans Langva Skarsvåg, Eskil Aursand, Jabir Ali Ouassou, Morten Hammer, Gunhild Reigstad, Åsmund Ervik, Eirik Holm Fyhn, Magnus Aa. Gjennestad, Peder Aursand and Øivind WilhelmsenJournal of Loss Prevention in the Process Industries 69 104354 (2021)
DOI: 10.1016/j.jlp.2020.104354
See this article
Flexible and efficient discretizations of multilayer models with variable density
José Garres-Díaz and Luca BonaventuraApplied Mathematics and Computation 402 126097 (2021)
DOI: 10.1016/j.amc.2021.126097
See this article
An approximate Riemann solver for shallow water equations and heat advection in horizontal centrifugal casting
Jan Boháček, Abdellah Kharicha, Andreas Ludwig and Menghuai WuApplied Mathematics and Computation 267 179 (2015)
DOI: 10.1016/j.amc.2015.04.028
See this article
A surrogate model for efficient quantification of uncertainties in multilayer shallow water flows
Alia Al-Ghosoun, Nabil El Moçayd and Mohammed SeaidEnvironmental Modelling & Software 144 105176 (2021)
DOI: 10.1016/j.envsoft.2021.105176
See this article
Viscous transfer of momentum across a shallow laminar flow
O. Devauchelle, P. Popović and E. LajeunesseJournal of Fluid Mechanics 932 (2022)
DOI: 10.1017/jfm.2021.1021
See this article
An Arbitrary High Order Well-Balanced ADER-DG Numerical Scheme for the Multilayer Shallow-Water Model with Variable Density
E. Guerrero Fernández, M. J. Castro Díaz, M. Dumbser and T. Morales de LunaJournal of Scientific Computing 90 (1) (2022)
DOI: 10.1007/s10915-021-01734-2
See this article
A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers
S. Busto and M. DumbserApplied Numerical Mathematics 175 108 (2022)
DOI: 10.1016/j.apnum.2022.02.005
See this article
Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime
Emmanuel Audusse, Léa Boittin and Martin ParisotESAIM: Mathematical Modelling and Numerical Analysis 55 (4) 1635 (2021)
DOI: 10.1051/m2an/2021031
See this article
Validation of the low dissipation computational algorithm CABARET-MFSH for multilayer hydrostatic flows with a free surface on the lock-release experiments
V.M. Goloviznin, Pavel A. Maiorov, Petr A. Maiorov and A.V. SolovjevJournal of Computational Physics 463 111239 (2022)
DOI: 10.1016/j.jcp.2022.111239
See this article
291 (2022)
DOI: 10.1007/978-981-16-9665-7_10
See this article
A memristive non-smooth dynamical system with coexistence of bimodule periodic oscillation
Yang Yang, Minglin Ma, Zhijun Li, Mengjiao Wang, Yichuang Sun and Liang ChenAEU - International Journal of Electronics and Communications 153 154279 (2022)
DOI: 10.1016/j.aeue.2022.154279
See this article
163 (2022)
DOI: 10.1002/9781119986607.ch6
See this article