ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

Salt-Wedge Response to Variable River Flow and Sea-Level Rise in the Microtidal Rječina River Estuary, Croatia

Nino Krvavica, Vanja Travaš and Nevenka Ožanić
Journal of Coastal Research 33 (4) 802 (2017)
DOI: 10.2112/JCOASTRES-D-16-00053.1
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A central scheme for shallow water flows along channels with irregular geometry

Jorge Balbás and Smadar Karni
ESAIM: Mathematical Modelling and Numerical Analysis 43 (2) 333 (2009)
DOI: 10.1051/m2an:2008050
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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. Tai
Physics of Fluids 26 (10) 103303 (2014)
DOI: 10.1063/1.4898563
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A numerical method for the two layer shallow water equations with dry states

Kyle T. Mandli
Ocean Modelling 72 80 (2013)
DOI: 10.1016/j.ocemod.2013.08.001
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Schéma nonlinéaire pour l'approximation numérique d'un système hyperbolique non conservatif

Christophe Berthon
Comptes Rendus Mathematique 335 (12) 1069 (2002)
DOI: 10.1016/S1631-073X(02)02615-8
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Shallow Water Flows in Channels

Gerardo Hernández-Dueñas and Smadar Karni
Journal of Scientific Computing 48 (1-3) 190 (2011)
DOI: 10.1007/s10915-010-9430-x
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InCIEC 2013

Farhan Haron Nuryazmeen, Tahir Wardah and Irma Noorazurah Mohamad
InCIEC 2013 343 (2014)
DOI: 10.1007/978-981-4585-02-6_30
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Global stability of weak solutions for a multilayer Saint–Venant model with interactions between layers

Bernard Di Martino, Boris Haspot and Yohan Penel
Nonlinear Analysis 163 177 (2017)
DOI: 10.1016/j.na.2017.07.010
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A Hybrid Method to Solve Shallow Water Flows with Horizontal Density Gradients

Gerardo Hernandez-Duenas
Journal of Scientific Computing 73 (2-3) 753 (2017)
DOI: 10.1007/s10915-017-0553-1
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Numerical methods with controlled dissipation for small-scale dependent shocks

Philippe G. LeFloch and Siddhartha Mishra
Acta Numerica 23 743 (2014)
DOI: 10.1017/S0962492914000099
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Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

François Bouchut
Edited Series on Advances in Nonlinear Science and Complexity, Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances 2 189 (2007)
DOI: 10.1016/S1574-6909(06)02004-1
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Analyzing the tidal-related origin of subinertial flows through the Strait of Gibraltar

M. Bruno, J. Macías, J. M. González-Vida and A. Vázquez
Journal of Geophysical Research 115 (C12) C12075 (2010)
DOI: 10.1029/2010JC006499
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A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows

M.J. Castro, J.A. García-Rodríguez, J.M. González-Vida and C. Parés
Computer Methods in Applied Mechanics and Engineering 195 (19-22) 2788 (2006)
DOI: 10.1016/j.cma.2005.07.007
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Central-Upwind Schemes for Two-Layer Shallow Water Equations

Alexander Kurganov and Guergana Petrova
SIAM Journal on Scientific Computing 31 (3) 1742 (2009)
DOI: 10.1137/080719091
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Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes

Manuel J. Castro, Philippe G. LeFloch, María Luz Muñoz-Ruiz and Carlos Parés
Journal of Computational Physics 227 (17) 8107 (2008)
DOI: 10.1016/j.jcp.2008.05.012
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The space–time CE/SE method for solving single and two-phase shallow flow models

Shamsul Qamar, Saqib Zia and Waqas Ashraf
Computers & Fluids 96 136 (2014)
DOI: 10.1016/j.compfluid.2014.03.015
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Extension of ENO and WENO schemes to one-dimensional sediment transport equations

N. Črnjarić-Žic, S. Vuković and L. Sopta
Computers & Fluids 33 (1) 31 (2004)
DOI: 10.1016/S0045-7930(03)00032-X
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The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems

M.J. Castro, A.M. Ferreiro Ferreiro, J.A. García-Rodríguez, et al.
Mathematical and Computer Modelling 42 (3-4) 419 (2005)
DOI: 10.1016/j.mcm.2004.01.016
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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. Parés
Journal of Scientific Computing 48 (1-3) 117 (2011)
DOI: 10.1007/s10915-011-9465-7
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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-Marie
Journal of Computational Physics 230 (9) 3453 (2011)
DOI: 10.1016/j.jcp.2011.01.042
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A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows

François Bouchut and Tomás Morales de Luna
SIAM Journal on Numerical Analysis 48 (5) 1733 (2010)
DOI: 10.1137/090758416
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An efficient splitting technique for two-layer shallow-water model

Christophe Berthon, Françoise Foucher and Tomás Morales
Numerical Methods for Partial Differential Equations 31 (5) 1396 (2015)
DOI: 10.1002/num.21949
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Multilayer Saint-Venant equations over movable beds

Mohammed Seaid, Jacques Sainte-Marie, Fayssal Benkhaldoun and Emmanuel Audusse
Discrete and Continuous Dynamical Systems - Series B 15 (4) 917 (2011)
DOI: 10.3934/dcdsb.2011.15.917
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On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems

Carlos Parés and Manuel Castro
ESAIM: Mathematical Modelling and Numerical Analysis 38 (5) 821 (2004)
DOI: 10.1051/m2an:2004041
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A positivity preserving central scheme for shallow water flows in channels with wet-dry states

Jorge Balbás and Gerardo Hernandez-Duenas
ESAIM: Mathematical Modelling and Numerical Analysis 48 (3) 665 (2014)
DOI: 10.1051/m2an/2013106
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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)
DOI: 10.1016/j.euromechflu.2011.07.002
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Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods

M.J. Castro Díaz, E.D. Fernández-Nieto and A.M. Ferreiro
Computers & Fluids 37 (3) 299 (2008)
DOI: 10.1016/j.compfluid.2007.07.017
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On an one-dimensional bi-layer shallow-water problem

Marı́a Luz Muñoz-Ruiz, Manuel Jesús Castro-Dı́az and Carlos Parés
Nonlinear Analysis: Theory, Methods & Applications 53 (5) 567 (2003)
DOI: 10.1016/S0362-546X(02)00137-2
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Parallel Computational Fluid Dynamics 2004

M.J. Gastro, J.A. García-Rodríguez, J.M. González-Vida and C. Parés
Parallel Computational Fluid Dynamics 2004 199 (1996)
DOI: 10.1016/B978-044452024-1/50026-9
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Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes

M.J. Castro Dı´az, E.D. Fernández-Nieto, A.M. Ferreiro and C. Parés
Computer Methods in Applied Mechanics and Engineering 198 (33-36) 2520 (2009)
DOI: 10.1016/j.cma.2009.03.001
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Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing

H. Alemi Ardakani, T.J. Bridges and M.R. Turner
Journal of Fluids and Structures 59 432 (2015)
DOI: 10.1016/j.jfluidstructs.2015.10.002
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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-Madroñal
Journal of Scientific Computing 48 (1-3) 16 (2011)
DOI: 10.1007/s10915-010-9427-5
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Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help

S. Cordier, M.H. Le and T. Morales de Luna
Advances in Water Resources 34 (8) 980 (2011)
DOI: 10.1016/j.advwatres.2011.05.002
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A treatment of discontinuities for nonlinear systems with linearly degenerate fields

Enrique D. Fernández-Nieto and Vicente Martínez
Computers & Fluids 36 (5) 987 (2007)
DOI: 10.1016/j.compfluid.2006.08.003
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A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods

M. J. Castro Díaz and E. Fernández-Nieto
SIAM Journal on Scientific Computing 34 (4) A2173 (2012)
DOI: 10.1137/100795280
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On Well‐Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems

M. J. Castro Díaz, T. Chacón Rebollo, E. D. Fernández‐Nieto and Carlos Parés
SIAM Journal on Scientific Computing 29 (3) 1093 (2007)
DOI: 10.1137/040607642
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A Roe-type scheme for two-phase shallow granular flows over variable topography

Marica Pelanti, François Bouchut and Anne Mangeney
ESAIM: Mathematical Modelling and Numerical Analysis 42 (5) 851 (2008)
DOI: 10.1051/m2an:2008029
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A robust finite volume model to simulate granular flows

S. Yavari-Ramshe, B. Ataie-Ashtiani and B.F. Sanders
Computers and Geotechnics 66 96 (2015)
DOI: 10.1016/j.compgeo.2015.01.015
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A fast adaptive quadtree scheme for a two-layer shallow water model

Wei-Koon Lee, Alistair G.L. Borthwick and Paul H. Taylor
Journal of Computational Physics 230 (12) 4848 (2011)
DOI: 10.1016/j.jcp.2011.03.007
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Efficient well-balanced hydrostatic upwind schemes for shallow-water equations

Christophe Berthon and Françoise Foucher
Journal of Computational Physics 231 (15) 4993 (2012)
DOI: 10.1016/j.jcp.2012.02.031
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A new composite scheme for two-layer shallow water flows with shocks

Nouh Izem, Fayssal Benkhaldoun, Slah Sahmim, Mohammed Seaid and Mohamed Wakrim
Journal of Applied Mathematics and Computing 44 (1-2) 467 (2014)
DOI: 10.1007/s12190-013-0703-z
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Solving shallow-water systems in 2D domains using Finite Volume methods and multimedia SSE instructions

M.J. Castro, J.A. García-Rodríguez, J.M. González-Vida and C. Parés
Journal of Computational and Applied Mathematics 221 (1) 16 (2008)
DOI: 10.1016/j.cam.2007.10.034
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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-Marie
ESAIM: Mathematical Modelling and Numerical Analysis 45 (1) 169 (2011)
DOI: 10.1051/m2an/2010036
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A meshless method for numerical simulation of depth-averaged turbulence flows using ak-ϵmodel

Yasser Alhuri, Fayssal Benkhaldoun, Driss Ouazar, Mohammed Seaid and Ahmed Taik
International Journal for Numerical Methods in Fluids 80 (1) 3 (2016)
DOI: 10.1002/fld.4067
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A two-layer model for simulating landslide dam over mobile river beds

Wei Liu and Siming He
Landslides 13 (3) 565 (2016)
DOI: 10.1007/s10346-015-0585-2
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Path-conservative central-upwind schemes for nonconservative hyperbolic systems

Manuel Jesús Castro Díaz, Alexander Kurganov and Tomás Morales de Luna
ESAIM: Mathematical Modelling and Numerical Analysis 53 (3) 959 (2019)
DOI: 10.1051/m2an/2018077
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Three-Layer Approximation of Two-Layer Shallow Water Equations

Alina Chertock, Alexander Kurganov, Zhuolin Qu and Tong Wu
Mathematical Modelling and Analysis 18 (5) 675 (2013)
DOI: 10.3846/13926292.2013.869269
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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. Cordier
Computers & Fluids 91 87 (2014)
DOI: 10.1016/j.compfluid.2013.11.031
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Air entrainment in transient flows in closed water pipes : A two-layer approach

C. Bourdarias, M. Ersoy and Stéphane Gerbi
ESAIM: Mathematical Modelling and Numerical Analysis 47 (2) 507 (2013)
DOI: 10.1051/m2an/2012036
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Finite-volume schemes for shallow-water equations

Alexander Kurganov
Acta Numerica 27 289 (2018)
DOI: 10.1017/S0962492918000028
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Two-layer shallow water computation of mud flow intrusions into quiescent water

Su-Chin Chen, Szu-Hsien Peng and Hervé Capart
Journal of Hydraulic Research 45 (1) 13 (2007)
DOI: 10.1080/00221686.2007.9521739
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Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues

M.J. Castro, T. Morales de Luna and C. Parés
Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues 18 131 (2017)
DOI: 10.1016/bs.hna.2016.10.002
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FRONT TRACKING FOR SCALAR BALANCE EQUATIONS

K. H. KARLSEN, N. H. RISEBRO and J. D. TOWERS
Journal of Hyperbolic Differential Equations 01 (01) 115 (2004)
DOI: 10.1142/S0219891604000068
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A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions

Manuel J. Castro, Jorge Macı́as, Carlos Parés, Jose A. Garcı́a-Rodrı́guez and Elena Vázquez-Cendón
Communications in Nonlinear Science and Numerical Simulation 9 (2) 241 (2004)
DOI: 10.1016/S1007-5704(03)00115-1
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A fast finite volume solver for multi-layered shallow water flows with mass exchange

Emmanuel Audusse, Fayssal Benkhaldoun, Saida Sari, Mohammed Seaid and Pablo Tassi
Journal of Computational Physics 272 23 (2014)
DOI: 10.1016/j.jcp.2014.04.026
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Numerical scheme for multilayer shallow-water model in the low-Froude number regime

Martin Parisot and Jean-Paul Vila
Comptes Rendus Mathematique 352 (11) 953 (2014)
DOI: 10.1016/j.crma.2014.09.020
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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 Mangeney
Journal of Computational Physics 230 (3) 515 (2011)
DOI: 10.1016/j.jcp.2010.10.001
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Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems

Manuel J. Castro, Ulrik S. Fjordholm, Siddhartha Mishra and Carlos Parés
SIAM Journal on Numerical Analysis 51 (3) 1371 (2013)
DOI: 10.1137/110845379
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An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment

François Bouchut and Tomás Morales de Luna
ESAIM: Mathematical Modelling and Numerical Analysis 42 (4) 683 (2008)
DOI: 10.1051/m2an:2008019
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Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar

Manuel J. Castro, José A. García-Rodríguez, José M. González-Vida, Jorge Macías and Carlos Parés
Advances in Engineering Software 38 (6) 386 (2007)
DOI: 10.1016/j.advengsoft.2006.09.012
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A Finite Difference Method for Piecewise Deterministic Processes with Memory. II

M. Annunziato
Mathematical Modelling and Analysis 14 (2) 139 (2009)
DOI: 10.3846/1392-6292.2009.14.139-158
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First- and second-order finite volume methods for the one-dimensional nonconservative Euler system

Stéphane Clain and David Rochette
Journal of Computational Physics 228 (22) 8214 (2009)
DOI: 10.1016/j.jcp.2009.07.038
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Godunov method for nonconservative hyperbolic systems

María Luz Muñoz-Ruiz and Carlos Parés
ESAIM: Mathematical Modelling and Numerical Analysis 41 (1) 169 (2007)
DOI: 10.1051/m2an:2007011
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Numerical simulation of two-layer shallow water flows through channels with irregular geometry

Manuel J. Castro, José A. Garcı́a-Rodrı́guez, José M. González-Vida, et al.
Journal of Computational Physics 195 (1) 202 (2004)
DOI: 10.1016/j.jcp.2003.08.035
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A simple multi-layer finite volume solver for density-driven shallow water flows

Fayssal Benkhaldoun, Saida Sari and Mohammed Seaid
Mathematics and Computers in Simulation 99 170 (2014)
DOI: 10.1016/j.matcom.2013.04.016
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Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts

M. Dudzinski and M. Lukáčová-Medvid’ová
Journal of Computational Physics 235 82 (2013)
DOI: 10.1016/j.jcp.2012.10.037
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Dynamics of surface and internal long waves generated by atmospheric pressure disturbances

Young-Kwang Choi and Tae-Chang Jo
Applied Ocean Research 76 61 (2018)
DOI: 10.1016/j.apor.2018.04.010
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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 Zhang
Comptes Rendus Mécanique 343 (7-8) 429 (2015)
DOI: 10.1016/j.crme.2015.05.002
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A rigorous finite volume model to simulate subaerial and submarine landslide-generated waves

S. Yavari-Ramshe and B. Ataie-Ashtiani
Landslides 14 (1) 203 (2017)
DOI: 10.1007/s10346-015-0662-6
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Regularized Equations for Numerical Simulation of Flows in the Two-Layer Shallow Water Approximation

T. G. Elizarova and A. V. Ivanov
Computational Mathematics and Mathematical Physics 58 (5) 714 (2018)
DOI: 10.1134/S0965542518050081
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NUMERICAL TREATMENT OF WET/DRY FRONTS IN SHALLOW FLOWS WITH A MODIFIED ROE SCHEME

MANUEL J. CASTRO, JOSÉ M. GONZÁLEZ-VIDA and CARLOS PARÉS
Mathematical Models and Methods in Applied Sciences 16 (06) 897 (2006)
DOI: 10.1142/S021820250600139X
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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. Tai
Advances in Water Resources 100 183 (2017)
DOI: 10.1016/j.advwatres.2016.12.014
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A two-layer model for the intrusion of two-phase debris flow into a river

Wei Liu and Siming He
Quarterly Journal of Engineering Geology and Hydrogeology 51 (1) 113 (2018)
DOI: 10.1144/qjegh2017-071
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An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification

F. Couderc, A. Duran and J.-P. Vila
Journal of Computational Physics 343 235 (2017)
DOI: 10.1016/j.jcp.2017.04.018
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WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE

MANUEL J. CASTRO, ALBERTO PARDO MILANÉS and CARLOS PARÉS
Mathematical Models and Methods in Applied Sciences 17 (12) 2055 (2007)
DOI: 10.1142/S021820250700256X
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CONSERVATION LAWS FOR ONE-DIMENSIONAL SHALLOW WATER MODELS FOR ONE AND TWO-LAYER FLOWS

RICARDO BARROS
Mathematical Models and Methods in Applied Sciences 16 (01) 119 (2006)
DOI: 10.1142/S0218202506001078
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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 Ožanić
Journal of Hydrology and Hydromechanics 65 (1) (2017)
DOI: 10.1515/johh-2016-0039
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Simplified two-layer models of precipitating atmosphere and their properties

J. Lambaerts, G. Lapeyre, V. Zeitlin and F. Bouchut
Physics of Fluids 23 (4) 046603 (2011)
DOI: 10.1063/1.3582356
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Central Schemes for Nonconservative Hyperbolic Systems

M. J. Castro, Carlos Parés, Gabriella Puppo and Giovanni Russo
SIAM Journal on Scientific Computing 34 (5) B523 (2012)
DOI: 10.1137/110828873
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Approximate Osher–Solomon schemes for hyperbolic systems

Manuel J. Castro, José M. Gallardo and Antonio Marquina
Applied Mathematics and Computation 272 347 (2016)
DOI: 10.1016/j.amc.2015.06.104
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Numerical methods for nonconservative hyperbolic systems: a theoretical framework.

Carlos Parés
SIAM Journal on Numerical Analysis 44 (1) 300 (2006)
DOI: 10.1137/050628052
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Two-Layer Shallow Water System: A Relaxation Approach

Rémi Abgrall and Smadar Karni
SIAM Journal on Scientific Computing 31 (3) 1603 (2009)
DOI: 10.1137/06067167X
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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)
DOI: 10.1016/j.ijrmms.2016.10.006
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Discontinuous Galerkin method for solving incompressible two-phase shallow granular flow model

Muhammad Rehan Saleem, Ubaid Ahmed Nisar and Shamsul Qamar
Advances in Mechanical Engineering 11 (9) 168781401987490 (2019)
DOI: 10.1177/1687814019874908
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Entropy-stable space–time DG schemes for non-conservative hyperbolic systems

Andreas Hiltebrand, Siddhartha Mishra and Carlos Parés
ESAIM: Mathematical Modelling and Numerical Analysis 52 (3) 995 (2018)
DOI: 10.1051/m2an/2017056
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Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

M. Rehan Saleem, Ishtiaq Ali and Shamsul Qamar
Results in Physics 8 379 (2018)
DOI: 10.1016/j.rinp.2017.12.044
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Quasi-gasdynamic algorithm for numerical solution of two-layer shallow water equations

Tatiana Gennadyevna Elizarova and Aleksander Vladimirovich Ivanov
Keldysh Institute Preprints (69) 1 (2016)
DOI: 10.20948/prepr-2016-69
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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 Dumbser
Monthly Notices of the Royal Astronomical Society 477 (2) 2251 (2018)
DOI: 10.1093/mnras/sty542
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Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity

Nino Krvavica, Miran Tuhtan and Gordan Jelenić
Advances in Water Resources 122 187 (2018)
DOI: 10.1016/j.advwatres.2018.10.017
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A Godunov method for the computation of erosional shallow water transients

L. Fraccarollo, H. Capart and Y. Zech
International Journal for Numerical Methods in Fluids 41 (9) 951 (2003)
DOI: 10.1002/fld.475
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Finite-Volume Solvers for a Multilayer Saint-Venant System

Emmanuel Audusse and Marie-Odile Bristeau
International Journal of Applied Mathematics and Computer Science 17 (3) 311 (2007)
DOI: 10.2478/v10006-007-0025-0
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Numerical Mathematics and Advanced Applications

M. J. Castro, J. A. García, J. M. González and C. Parés
Numerical Mathematics and Advanced Applications 288 (2006)
DOI: 10.1007/978-3-540-34288-5_22
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Hyperbolic Problems: Theory, Numerics, Applications

M. Pelanti, F. Bouchut, A. Mangeney and J. -P. Vilotte
Hyperbolic Problems: Theory, Numerics, Applications 825 (2008)
DOI: 10.1007/978-3-540-75712-2_85
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Mathematical and Numerical Aspects of Wave Propagation WAVES 2003

M. J. Castro, J. A. García-Rodríguez, J. M. González-Vida, et al.
Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 529 (2003)
DOI: 10.1007/978-3-642-55856-6_85
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Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form

Abdelaziz Beljadid, Philippe G. LeFloch, Siddhartha Mishra and Carlos Parés
Communications in Computational Physics 21 (4) 913 (2017)
DOI: 10.4208/cicp.OA-2016-0019
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An alternative model of multicomponent diffusion based on a combination of the Maxwell-Stefan theory and continuum mechanics

Jan Franců and Jiří Mikyška
Journal of Computational Physics 400 108962 (2020)
DOI: 10.1016/j.jcp.2019.108962
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Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

Manuel Jesús Castro Diaz, Yuanzhen Cheng, Alina Chertock and Alexander Kurganov
Communications in Computational Physics 16 (5) 1323 (2014)
DOI: 10.4208/cicp.180513.230514a
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A central-upwind scheme with artificial viscosity for shallow-water flows in channels

Gerardo Hernandez-Duenas and Abdelaziz Beljadid
Advances in Water Resources 96 323 (2016)
DOI: 10.1016/j.advwatres.2016.07.021
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Re-evaluating efficiency of first-order numerical schemes for two-layer shallow water systems by considering different eigenvalue solutions

Nino Krvavica
Advances in Water Resources 137 103508 (2020)
DOI: 10.1016/j.advwatres.2020.103508
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Efficient modeling of shallow water equations using method of lines and artificial viscosity

Mohamed M. Mousa and Wen-Xiu Ma
Modern Physics Letters B 34 (04) 2050051 (2020)
DOI: 10.1142/S0217984920500517
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