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A robust numerical scheme based on auxiliary interface variables and monotone-preserving reconstructions for two-layer shallow water equations with wet–dry fronts
Ernesto Pimentel‐García, Manuel J. Castro, Christophe Chalons and Carlos Parés Numerical Methods for Partial Differential Equations 40(6) (2024) https://doi.org/10.1002/num.23133
Numerical Schemes for Coupled Systems of Nonconservative Hyperbolic Equations
Niklas Kolbe, Michael Herty and Siegfried Müller SIAM Journal on Numerical Analysis 62(5) 2143 (2024) https://doi.org/10.1137/23M1615176
Weakly Compressible Two-Layer Shallow-Water Flows Along Channels
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. Souillé Journal 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
Artificial Viscosity to Get Both Robustness and Discrete Entropy Inequalities
Christophe Berthon, Manuel J. Castro Díaz, Arnaud Duran, Tomás Morales de Luna and Khaled Saleh Journal of Scientific Computing 97(3) (2023) https://doi.org/10.1007/s10915-023-02385-1
On well-balanced implicit-explicit Lagrange-projection schemes for two-layer shallow water equations
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 Parés Journal of Computational Physics 459 111152 (2022) https://doi.org/10.1016/j.jcp.2022.111152
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 Du Water 14(21) 3562 (2022) https://doi.org/10.3390/w14213562
Well-balanced numerical resolution of the two-layer shallow water equations under rigid-lid with wet–dry fronts
Recent Advances in Numerical Methods for Hyperbolic PDE Systems
José M. Gallardo, Manuel J. Castro and Antonio Marquina SEMA 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
A fifth order WENO scheme for numerical simulation of shallow granular two-phase flow model
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 Koellermeier Applied Mathematics and Computation 388 125544 (2021) https://doi.org/10.1016/j.amc.2020.125544
A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels
Gerardo Hernandez-Duenas and Jorge Balbás ESAIM: Mathematical Modelling and Numerical Analysis 55(5) 2185 (2021) https://doi.org/10.1051/m2an/2021052
A surrogate model for efficient quantification of uncertainties in multilayer shallow water flows
Nonlinear stability of two-layer shallow water flows with a free surface
Francisco de Melo Viríssimo and Paul A. Milewski Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476(2236) (2020) https://doi.org/10.1098/rspa.2019.0594
Efficient modeling of shallow water equations using method of lines and artificial viscosity
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 Luna Mathematics 8(5) 848 (2020) https://doi.org/10.3390/math8050848
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-Navarro Journal of Hydroinformatics 22(5) 972 (2020) https://doi.org/10.2166/hydro.2020.207
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 Luna ESAIM: 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
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) 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 Dumbser Monthly Notices of the Royal Astronomical Society 477(2) 2251 (2018) https://doi.org/10.1093/mnras/sty542
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) 49 (2017) https://doi.org/10.1515/johh-2016-0039
A Hybrid Method to Solve Shallow Water Flows with Horizontal Density Gradients
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) https://doi.org/10.1016/bs.hna.2016.10.002
Some considerations on numerical schemes for treating hyperbolicity issues in two-layer models
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) https://doi.org/10.4208/cicp.OA-2016-0019
Salt-Wedge Response to Variable River Flow and Sea-Level Rise in the Microtidal Rječina River Estuary, Croatia
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 Taik International Journal for Numerical Methods in Fluids 80(1) 3 (2016) https://doi.org/10.1002/fld.4067
Quasi-gasdynamic algorithm for numerical solution of two-layer shallow water equations
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) https://doi.org/10.1016/j.jcp.2014.04.026
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) https://doi.org/10.4208/cicp.180513.230514a
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) https://doi.org/10.1051/m2an/2013106
A simple multi-layer finite volume solver for density-driven shallow water flows
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) https://doi.org/10.1137/110845379
Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts
THREE-LAYER APPROXIMATION OF TWO-LAYER SHALLOW WATER EQUATIONS
Alina Chertock, Alexander Kurganov, Alexander Kurganov, Zhuolin Qu and Tong Wu Mathematical Modelling and Analysis 18(5) 675 (2013) https://doi.org/10.3846/13926292.2013.869269
A Shallow Water model for the numerical simulation of overland flow on surfaces with ridges and furrows
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) https://doi.org/10.1137/110828873
A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
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) 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
Multilayer Saint-Venant equations over movable beds
Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie and Mohammed Seaid Discrete & Continuous Dynamical Systems - B 15(4) 917 (2011) https://doi.org/10.3934/dcdsb.2011.15.917
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) https://doi.org/10.1051/m2an/2010036
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System