A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system
ESAIM: M2AN, 35 1 (2001) 107-127
Published online: 2002-04-15
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):
A Well-Balanced Wet–Dry Front Reconstruction for Two-Layer Shallow Water Flows
Xue WangMathematics 14 (4) 595 (2026)
https://doi.org/10.3390/math14040595
(2026)
https://doi.org/10.2139/ssrn.6203413
Semi-implicit fully exactly well-balanced schemes for the two-layer shallow water system
C. Caballero-Cárdenas, M.J. Castro, C. Chalons, T. Morales de Luna and M.L. Muñoz-RuizApplied Numerical Mathematics 218 128 (2025)
https://doi.org/10.1016/j.apnum.2025.07.014
High-order WENO finite-difference methods for hyperbolic nonconservative systems of partial differential equations
Baifen Ren and Carlos ParésJournal of Computational Physics 535 114047 (2025)
https://doi.org/10.1016/j.jcp.2025.114047
A numerical model for simulation of bedload transport in unsteady trans-critical river flow
Fabien Souillé, Nicolas Claude and Magali JodeauEnvironmental Modelling & Software 192 106531 (2025)
https://doi.org/10.1016/j.envsoft.2025.106531
25 (2025)
https://doi.org/10.1007/978-981-97-8152-2_2
Ill posedness in shallow multi-phase debris-flow models
Jake Langham, Xiannan Meng, Jamie P. Webb, Chris G. Johnson and J.M.N.T. GrayJournal of Fluid Mechanics 1015 (2025)
https://doi.org/10.1017/jfm.2025.10297
A semi-implicit exactly fully well-balanced relaxation scheme for the Shallow Water Linearized Moment Equations
C. Caballero-Cárdenas, I. Gómez-Bueno, A. Del Grosso, J. Koellermeier and T. Morales de LunaComputer Methods in Applied Mechanics and Engineering 437 117788 (2025)
https://doi.org/10.1016/j.cma.2025.117788
Numerical Schemes for Coupled Systems of Nonconservative Hyperbolic Equations
Niklas Kolbe, Michael Herty and Siegfried MüllerSIAM Journal on Numerical Analysis 62 (5) 2143 (2024)
https://doi.org/10.1137/23M1615176
A semi-Lagrangian Splitting framework for the simulation of non-hydrostatic free-surface flows
Andreas Alexandris-Galanopoulos, George Papadakis and Kostas BelibassakisOcean Modelling 187 102290 (2024)
https://doi.org/10.1016/j.ocemod.2023.102290
High-order compact gas-kinetic scheme for two-layer shallow water equations on unstructured mesh
Fengxiang Zhao, Jianping Gan and Kun XuJournal of Computational Physics 498 112651 (2024)
https://doi.org/10.1016/j.jcp.2023.112651
The Navier-Stokes system with temperature and salinity for free surface flows. Numerical scheme and validation
L. Boittin, F. Bouchut, M.-O. Bristeau, A. Mangeney, J. Sainte-Marie and F. SouilléJournal of Computational Physics 510 113065 (2024)
https://doi.org/10.1016/j.jcp.2024.113065
A modified Rusanov method for simulating two-layer shallow water flows with irregular topography
Kamel MohamedComputational and Applied Mathematics 43 (3) (2024)
https://doi.org/10.1007/s40314-024-02640-7
A robust numerical scheme based on auxiliary interface variables and monotone-preserving reconstructions for two-layer shallow water equations with wet–dry fronts
Jian Dong and Xu QianComputers & Fluids 272 106193 (2024)
https://doi.org/10.1016/j.compfluid.2024.106193
The Riemann problem for two-layer shallow water equations with bottom topography
Fan Wang, Wancheng Sheng, Yanbo Hu and Qinglong ZhangAdvances in Nonlinear Analysis 13 (1) (2024)
https://doi.org/10.1515/anona-2024-0058
Weakly Compressible Two-Layer Shallow-Water Flows Along Channels
Sarswati Shah and Gerardo Hernández-DueñasJournal of Scientific Computing 100 (3) (2024)
https://doi.org/10.1007/s10915-024-02608-z
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method
Ernesto Pimentel‐García, Manuel J. Castro, Christophe Chalons and Carlos ParésNumerical Methods for Partial Differential Equations 40 (6) (2024)
https://doi.org/10.1002/num.23133
Flux globalization based well-balanced path-conservative central-upwind scheme for two-layer thermal rotating shallow water equations
Yangyang Cao, Alexander Kurganov, Yongle Liu and Vladimir ZeitlinJournal of Computational Physics 474 111790 (2023)
https://doi.org/10.1016/j.jcp.2022.111790
On well-balanced implicit-explicit Lagrange-projection schemes for two-layer shallow water equations
A. Del Grosso, M. Castro Díaz, C. Chalons and T. Morales de LunaApplied Mathematics and Computation 442 127702 (2023)
https://doi.org/10.1016/j.amc.2022.127702
Discussion on different numerical treatments on the loss of hyperbolicity for the two-layer shallow water system
M.J. Castro Díaz, E.D. Fernández-Nieto, J. Garres-Díaz and T. Morales de LunaAdvances in Water Resources 182 104587 (2023)
https://doi.org/10.1016/j.advwatres.2023.104587
Artificial Viscosity to Get Both Robustness and Discrete Entropy Inequalities
Christophe Berthon, Manuel J. Castro Díaz, Arnaud Duran, Tomás Morales de Luna and Khaled SalehJournal of Scientific Computing 97 (3) (2023)
https://doi.org/10.1007/s10915-023-02385-1
In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension
Ernesto Pimentel-García, Manuel J. Castro, Christophe Chalons, Tomás Morales de Luna and Carlos ParésJournal of Computational Physics 459 111152 (2022)
https://doi.org/10.1016/j.jcp.2022.111152
Fifth-order A-WENO schemes based on the path-conservative central-upwind method
Shaoshuai Chu, Alexander Kurganov and Mingye NaJournal of Computational Physics 469 111508 (2022)
https://doi.org/10.1016/j.jcp.2022.111508
Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for Two-Layer Thermal Rotating Shallow Water Equations
Yangyang Cao, Alexander Kurganov, Yongle Liu and Vladimir ZeitlinSSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4089079
Well-balanced numerical resolution of the two-layer shallow water equations under rigid-lid with wet–dry fronts
Ralph LteifComputers & Fluids 235 105277 (2022)
https://doi.org/10.1016/j.compfluid.2021.105277
An Analytical Solution to Predict the Distribution of Streamwise Flow Velocity in an Ecological River with Submerged Vegetation
Jiao Zhang, Zhangyi Mi, Wen Wang, Zhanbin Li, Huilin Wang, Qingjing Wang, Xunle Zhang and Xinchun DuWater 14 (21) 3562 (2022)
https://doi.org/10.3390/w14213562
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)
https://doi.org/10.1007/s10915-021-01734-2
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)
https://doi.org/10.1016/j.envsoft.2021.105176
Recent Advances in Numerical Methods for Hyperbolic PDE Systems
José M. Gallardo, Manuel J. Castro and Antonio MarquinaSEMA SIMAI Springer Series, Recent Advances in Numerical Methods for Hyperbolic PDE Systems 28 3 (2021)
https://doi.org/10.1007/978-3-030-72850-2_1
On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems
Ernesto Pimentel-García, Carlos Parés, Manuel J. Castro and Julian KoellermeierApplied Mathematics and Computation 388 125544 (2021)
https://doi.org/10.1016/j.amc.2020.125544
A fifth order WENO scheme for numerical simulation of shallow granular two-phase flow model
Omar Rabbani, Saqib Zia and Asad RehmanAdvances in Mechanical Engineering 13 (9) (2021)
https://doi.org/10.1177/16878140211045240
A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels
Gerardo Hernandez-Duenas and Jorge BalbásESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2185 (2021)
https://doi.org/10.1051/m2an/2021052
Efficient modeling of shallow water equations using method of lines and artificial viscosity
Mohamed M. Mousa and Wen-Xiu MaModern Physics Letters B 34 (04) 2050051 (2020)
https://doi.org/10.1142/S0217984920500517
Re-evaluating efficiency of first-order numerical schemes for two-layer shallow water systems by considering different eigenvalue solutions
Nino KrvavicaAdvances in Water Resources 137 103508 (2020)
https://doi.org/10.1016/j.advwatres.2020.103508
An alternative model of multicomponent diffusion based on a combination of the Maxwell-Stefan theory and continuum mechanics
Jan Franců and Jiří MikyškaJournal of Computational Physics 400 108962 (2020)
https://doi.org/10.1016/j.jcp.2019.108962
Nonlinear stability of two-layer shallow water flows with a free surface
Francisco de Melo Viríssimo and Paul A. MilewskiProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2236) (2020)
https://doi.org/10.1098/rspa.2019.0594
Adaptation of flux-based solvers to 2D two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts
J. Murillo, S. Martinez-Aranda, A. Navas-Montilla and P. García-NavarroJournal of Hydroinformatics 22 (5) 972 (2020)
https://doi.org/10.2166/hydro.2020.207
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)
https://doi.org/10.3390/math8050848
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)
https://doi.org/10.1051/m2an/2019044
Path-conservative central-upwind schemes for nonconservative hyperbolic systems
Manuel Jesús Castro Díaz, Alexander Kurganov and Tomás Morales de LunaESAIM: Mathematical Modelling and Numerical Analysis 53 (3) 959 (2019)
https://doi.org/10.1051/m2an/2018077
Discontinuous Galerkin method for solving incompressible two-phase shallow granular flow model
Muhammad Rehan Saleem, Ubaid Ahmed Nisar and Shamsul QamarAdvances in Mechanical Engineering 11 (9) (2019)
https://doi.org/10.1177/1687814019874908
Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity
Nino Krvavica, Miran Tuhtan and Gordan JelenićAdvances in Water Resources 122 187 (2018)
https://doi.org/10.1016/j.advwatres.2018.10.017
Finite-volume schemes for shallow-water equations
Alexander KurganovActa Numerica 27 289 (2018)
https://doi.org/10.1017/S0962492918000028
Regularized Equations for Numerical Simulation of Flows in the Two-Layer Shallow Water Approximation
T. G. Elizarova and A. V. IvanovComputational Mathematics and Mathematical Physics 58 (5) 714 (2018)
https://doi.org/10.1134/S0965542518050081
Entropy-stable space–time DG schemes for non-conservative hyperbolic systems
Andreas Hiltebrand, Siddhartha Mishra and Carlos ParésESAIM: Mathematical Modelling and Numerical Analysis 52 (3) 995 (2018)
https://doi.org/10.1051/m2an/2017056
Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity
Elena Gaburro, Manuel J Castro and Michael DumbserMonthly Notices of the Royal Astronomical Society 477 (2) 2251 (2018)
https://doi.org/10.1093/mnras/sty542
Dynamics of surface and internal long waves generated by atmospheric pressure disturbances
Young-Kwang Choi and Tae-Chang JoApplied Ocean Research 76 61 (2018)
https://doi.org/10.1016/j.apor.2018.04.010
A two-layer model for the intrusion of two-phase debris flow into a river
Wei Liu and Siming HeQuarterly Journal of Engineering Geology and Hydrogeology 51 (1) 113 (2018)
https://doi.org/10.1144/qjegh2017-071
Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model
M. Rehan Saleem, Ishtiaq Ali and Shamsul QamarResults in Physics 8 379 (2018)
https://doi.org/10.1016/j.rinp.2017.12.044
A rigorous finite volume model to simulate subaerial and submarine landslide-generated waves
S. Yavari-Ramshe and B. Ataie-AshtianiLandslides 14 (1) 203 (2017)
https://doi.org/10.1007/s10346-015-0662-6
Some considerations on numerical schemes for treating hyperbolicity issues in two-layer models
L. Sarno, A. Carravetta, R. Martino, M.N. Papa and Y.-C. TaiAdvances in Water Resources 100 183 (2017)
https://doi.org/10.1016/j.advwatres.2016.12.014
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
M.J. Castro, T. Morales de Luna and C. ParésHandbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues 18 131 (2017)
https://doi.org/10.1016/bs.hna.2016.10.002
Salt-Wedge Response to Variable River Flow and Sea-Level Rise in the Microtidal Rječina River Estuary, Croatia
Nino Krvavica, Vanja Travaš and Nevenka OžanićJournal of Coastal Research 33 (4) 802 (2017)
https://doi.org/10.2112/JCOASTRES-D-16-00053.1
A Hybrid Method to Solve Shallow Water Flows with Horizontal Density Gradients
Gerardo Hernandez-DuenasJournal of Scientific Computing 73 (2-3) 753 (2017)
https://doi.org/10.1007/s10915-017-0553-1
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)
https://doi.org/10.1016/j.na.2017.07.010
The immersed-body gas-solid interaction model for blast analysis in fractured solid media
P. Yang, J. Xiang, M. Chen, et al.International Journal of Rock Mechanics and Mining Sciences 91 119 (2017)
https://doi.org/10.1016/j.ijrmms.2016.10.006
An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification
F. Couderc, A. Duran and J.-P. VilaJournal of Computational Physics 343 235 (2017)
https://doi.org/10.1016/j.jcp.2017.04.018
Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries: Finite volume solver and field validation
Nino Krvavica, Ivica Kožar, Vanja Travaš and Nevenka OžanićJournal of Hydrology and Hydromechanics 65 (1) 49 (2017)
https://doi.org/10.1515/johh-2016-0039
Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form
Abdelaziz Beljadid, Philippe G. LeFloch, Siddhartha Mishra and Carlos ParésCommunications in Computational Physics 21 (4) 913 (2017)
https://doi.org/10.4208/cicp.OA-2016-0019
Approximate Osher–Solomon schemes for hyperbolic systems
Manuel J. Castro, José M. Gallardo and Antonio MarquinaApplied Mathematics and Computation 272 347 (2016)
https://doi.org/10.1016/j.amc.2015.06.104
A central-upwind scheme with artificial viscosity for shallow-water flows in channels
Gerardo Hernandez-Duenas and Abdelaziz BeljadidAdvances in Water Resources 96 323 (2016)
https://doi.org/10.1016/j.advwatres.2016.07.021
A meshless method for numerical simulation of depth‐averaged turbulence flows using a k‐ϵ model
Yasser Alhuri, Fayssal Benkhaldoun, Driss Ouazar, Mohammed Seaid and Ahmed TaikInternational Journal for Numerical Methods in Fluids 80 (1) 3 (2016)
https://doi.org/10.1002/fld.4067
A two-layer model for simulating landslide dam over mobile river beds
Wei Liu and Siming HeLandslides 13 (3) 565 (2016)
https://doi.org/10.1007/s10346-015-0585-2
Quasi-gasdynamic algorithm for numerical solution of two-layer shallow water equations
Tatiana Gennadyevna Elizarova and Aleksander Vladimirovich IvanovKeldysh Institute Preprints (69) 1 (2016)
https://doi.org/10.20948/prepr-2016-69
Adaptation of f-wave finite volume methods to the two-layer shallow-water equations in a moving vessel with a rigid-lid
H. Alemi Ardakani, T.J. Bridges and M.R. TurnerJournal of Computational and Applied Mathematics 296 462 (2016)
https://doi.org/10.1016/j.cam.2015.09.026
A robust and well-balanced numerical model for solving the two-layer shallow water equations over uneven topography
Xinhua Lu, Bingjiang Dong, Bing Mao and Xiaofeng ZhangComptes Rendus. Mécanique 343 (7-8) 429 (2015)
https://doi.org/10.1016/j.crme.2015.05.002
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)
https://doi.org/10.1002/num.21949
A robust finite volume model to simulate granular flows
S. Yavari-Ramshe, B. Ataie-Ashtiani and B.F. SandersComputers and Geotechnics 66 96 (2015)
https://doi.org/10.1016/j.compgeo.2015.01.015
Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing
H. Alemi Ardakani, T.J. Bridges and M.R. TurnerJournal of Fluids and Structures 59 432 (2015)
https://doi.org/10.1016/j.jfluidstructs.2015.10.002
A two-layer depth-averaged approach to describe the regime stratification in collapses of dry granular columns
L. Sarno, A. Carravetta, R. Martino and Y. C. TaiPhysics of Fluids 26 (10) (2014)
https://doi.org/10.1063/1.4898563
Solving Two-Mode Shallow Water Equations Using Finite Volume Methods
Manuel Jesús Castro Diaz, Yuanzhen Cheng, Alina Chertock and Alexander KurganovCommunications in Computational Physics 16 (5) 1323 (2014)
https://doi.org/10.4208/cicp.180513.230514a
InCIEC 2013
Farhan Haron Nuryazmeen, Tahir Wardah and Irma Noorazurah MohamadInCIEC 2013 343 (2014)
https://doi.org/10.1007/978-981-4585-02-6_30
The space–time CE/SE method for solving single and two-phase shallow flow models
Shamsul Qamar, Saqib Zia and Waqas AshrafComputers & Fluids 96 136 (2014)
https://doi.org/10.1016/j.compfluid.2014.03.015
A new composite scheme for two-layer shallow water flows with shocks
Nouh Izem, Fayssal Benkhaldoun, Slah Sahmim, Mohammed Seaid and Mohamed WakrimJournal of Applied Mathematics and Computing 44 (1-2) 467 (2014)
https://doi.org/10.1007/s12190-013-0703-z
Numerical scheme for multilayer shallow-water model in the low-Froude number regime
Martin Parisot and Jean-Paul VilaComptes Rendus. Mathématique 352 (11) 953 (2014)
https://doi.org/10.1016/j.crma.2014.09.020
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)
https://doi.org/10.1016/j.matcom.2013.04.016
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)
https://doi.org/10.1016/j.jcp.2014.04.026
On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems
E.D. Fernández-Nieto, C. Lucas, T. Morales de Luna and S. CordierComputers & Fluids 91 87 (2014)
https://doi.org/10.1016/j.compfluid.2013.11.031
Numerical methods with controlled dissipation for small-scale dependent shocks
Philippe G. LeFloch and Siddhartha MishraActa Numerica 23 743 (2014)
https://doi.org/10.1017/S0962492914000099
A positivity preserving central scheme for shallow water flows in channels with wet-dry states
Jorge Balbás and Gerardo Hernandez-DuenasESAIM: Mathematical Modelling and Numerical Analysis 48 (3) 665 (2014)
https://doi.org/10.1051/m2an/2013106
Air entrainment in transient flows in closed water pipes : A two-layer approach
C. Bourdarias, M. Ersoy and Stéphane GerbiESAIM: Mathematical Modelling and Numerical Analysis 47 (2) 507 (2013)
https://doi.org/10.1051/m2an/2012036
Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems
Manuel J. Castro, Ulrik S. Fjordholm, Siddhartha Mishra and Carlos ParésSIAM Journal on Numerical Analysis 51 (3) 1371 (2013)
https://doi.org/10.1137/110845379
THREE-LAYER APPROXIMATION OF TWO-LAYER SHALLOW WATER EQUATIONS
Alina Chertock, Alexander Kurganov, Alexander Kurganov, Zhuolin Qu and Tong WuMathematical Modelling and Analysis 18 (5) 675 (2013)
https://doi.org/10.3846/13926292.2013.869269
Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts
M. Dudzinski and M. Lukáčová-Medvid’ováJournal of Computational Physics 235 82 (2013)
https://doi.org/10.1016/j.jcp.2012.10.037
A numerical method for the two layer shallow water equations with dry states
Kyle T. MandliOcean Modelling 72 80 (2013)
https://doi.org/10.1016/j.ocemod.2013.08.001
A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
M. J. Castro Díaz and E. Fernández-NietoSIAM Journal on Scientific Computing 34 (4) A2173 (2012)
https://doi.org/10.1137/100795280
A Shallow Water model for the numerical simulation of overland flow on surfaces with ridges and furrows
Ulrich Razafison, Stéphane Cordier, Olivier Delestre, et al.European Journal of Mechanics - B/Fluids 31 44 (2012)
https://doi.org/10.1016/j.euromechflu.2011.07.002
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
Christophe Berthon and Françoise FoucherJournal of Computational Physics 231 (15) 4993 (2012)
https://doi.org/10.1016/j.jcp.2012.02.031
Central Schemes for Nonconservative Hyperbolic Systems
M. J. Castro, Carlos Parés, Gabriella Puppo and Giovanni RussoSIAM Journal on Scientific Computing 34 (5) B523 (2012)
https://doi.org/10.1137/110828873
Shallow Water Flows in Channels
Gerardo Hernández-Dueñas and Smadar KarniJournal of Scientific Computing 48 (1-3) 190 (2011)
https://doi.org/10.1007/s10915-010-9430-x
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
Emmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame and Jacques Sainte-MarieESAIM: Mathematical Modelling and Numerical Analysis 45 (1) 169 (2011)
https://doi.org/10.1051/m2an/2010036
Multilayer Saint-Venant equations over movable beds
Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie and Mohammed SeaidDiscrete & Continuous Dynamical Systems - B 15 (4) 917 (2011)
https://doi.org/10.3934/dcdsb.2011.15.917
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System
M. J. Castro-Díaz, E. D. Fernández-Nieto, J. M. González-Vida and C. Parés-MadroñalJournal of Scientific Computing 48 (1-3) 16 (2011)
https://doi.org/10.1007/s10915-010-9427-5
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)
https://doi.org/10.1016/j.jcp.2011.01.042
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System
E. D. Fernández-Nieto, M. J. Castro Díaz and C. ParésJournal of Scientific Computing 48 (1-3) 117 (2011)
https://doi.org/10.1007/s10915-011-9465-7
Simplified two-layer models of precipitating atmosphere and their properties
J. Lambaerts, G. Lapeyre, V. Zeitlin and F. BouchutPhysics of Fluids 23 (4) (2011)
https://doi.org/10.1063/1.3582356
Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help
S. Cordier, M.H. Le and T. Morales de LunaAdvances in Water Resources 34 (8) 980 (2011)
https://doi.org/10.1016/j.advwatres.2011.05.002
A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers
Marica Pelanti, François Bouchut and Anne MangeneyJournal of Computational Physics 230 (3) 515 (2011)
https://doi.org/10.1016/j.jcp.2010.10.001
A fast adaptive quadtree scheme for a two-layer shallow water model
Wei-Koon Lee, Alistair G.L. Borthwick and Paul H. TaylorJournal of Computational Physics 230 (12) 4848 (2011)
https://doi.org/10.1016/j.jcp.2011.03.007
A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows
François Bouchut and Tomás Morales de LunaSIAM Journal on Numerical Analysis 48 (5) 1733 (2010)
https://doi.org/10.1137/090758416