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  2021 (2)
High-order well-balanced methods for systems of balance laws: a control-based approach. Gómez, I.; Castro, M.; and Parés, C. Applied Mathematics and Computation, 394: 125820. 2021.
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Well-balanced high-order finite difference methods for systems of balance laws. C. Parés, C. P. Journal of Computational Physics, 425: 109880. 2021.
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  2020 (1)
A two-dimensional method for a family of dispersive shallow water models. N. Aïssiouene, M. B.; E. Godlewski, A. M.; and C. Parés, J. S. SMAI Journal of Computational Mathematics, 6: 187-226. 2020.
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  2014 (1)
Relation between PVM schemes and simple Riemann solvers. Morales de Luna, T.; Díaz, Manuel J., C.; and Parés, C. Numerical Methods for Partial Differential Equations, 30(4): 1315-1341. mar 2014.
Relation between PVM schemes and simple Riemann solvers [link]Paper   bibtex   abstract  
  2013 (1)
Reliability of first order numerical schemes for solving shallow water system over abrupt topography. Morales de Luna, T.; Díaz, Manuel J., C.; and Parés, C. Applied Mathematics and Computation, 219(17): 9012–9032. 2013.
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  2012 (3)
A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport. Díaz, Manuel J., C.; Fernández Nieto, E. D.; Morales de Luna, T.; Narbona-Reina, G.; and Parés, C. ESAIM: Mathematical Modelling and Numerical Analysis, 47(1): 1–32. 2012.
A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport [link]Paper   bibtex  
Deslizamientos Submarinos y Tsunamis en el Mar de Alborán. Un Ejemplo de Modelización. Macías, Jorge; Fernández-Salas, L.; González-Vida, J.; Vázquez, J.; Díaz, Manuel J., C.; Bárcenas, P.; Díaz del Río, V.; Morales de Luna, T.; de la Asunción, M.; and Parés, C. Volume 6 of Temas de OceanografíaInstituto Español de Oceanografía, Avda. del Brasil, 31. 28020 Madrid, 2012.
Deslizamientos Submarinos y Tsunamis en el Mar de Alborán. Un Ejemplo de Modelización. [link]Paper   bibtex  
5. Díaz, Manuel J., C.; de la Asunción, M.; Macías, Jorge; Parés, C.; Fernández Nieto, E. D.; González-Vida, J.; and Morales de Luna, T. IFCP Riemann solver: Application to tsunami modelling using GPUs, pages 237-244. E.-Vázquez; A.-Hidalgo; P.-García; and L.-Cea, editor(s). CRC Press, 2012.
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  2011 (4)
A Duality Method for Sediment Transport Based on a Modified Meyer-Peter & Müller Mod. Morales de Luna, T.; Díaz, Manuel J., C.; and Parés, C. Journal of Scientific Computing, 48(1): 258-273. 2011.
A Duality Method for Sediment Transport Based on a Modified Meyer-Peter & Müller Mod [link]Paper   bibtex   abstract  
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water Syst. Díaz, Manuel J., C.; Fernández Nieto, E. D.; González Vida, J. M.; and Parés, C. Journal of Scientific Computing, 48(1): 16-40. 2011.
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water Syst [link]Paper   bibtex   abstract  
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System. Fernández Nieto, E. D.; Díaz, Manuel J., C.; and Parés, C. Journal of Scientific Computing, 48(1): 117-140. 2011.
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System [link]Paper   bibtex   abstract  
On the convergence and well-balanced property of path-conservative numerical schemes for systems of balance laws. Muñoz Ruiz, M.; and Parés, C. Journal of Scientific Computing, 48(1-3): 274-295. 2011.
On the convergence and well-balanced property of path-conservative numerical schemes for systems of balance laws [link]Paper   bibtex  
  2010 (2)
FORCE schemes on unstructured meshes II: Nonconservative hyperbolic systems. Dumbser, M.; Hidalgo, A.; Díaz, Manuel J., C.; Parés, C.; and Toro, E. Comput. Methods Appl. Mech. Engrg., 199(9-12): 625–647. 2010.
FORCE schemes on unstructured meshes II: Nonconservative hyperbolic systems [link]Paper   bibtex   abstract  
On some fast well-balanced first order solvers for nonconservative systems. Díaz, Manuel J., C.; Pardo, A.; Parés, C.; and Toro, E. MATHEMATICS OF COMPUTATION, 79(271): 1427–1472. 2010.
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  2009 (6)
ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows. Dumbser, M.; Díaz, Manuel J., C.; Parés, C.; and F.-Toro, E. Computers & Fluids, 38(9): 1731–1748. 2009.
ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows [link]Paper   bibtex   abstract  
High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems. Díaz, Manuel J., C.; Fernández Nieto, E. D.; Ferreiro, A.; García-Rodríguez, J. A.; and Parés, C. J. Sci. Comput., 39(1): 67–114. 2009.
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On a shallow water model for the simulation of turbidity currents. Morales de Luna, T.; Díaz, Manuel J., C.; Parés, C.; and Fernández Nieto, E. D. Communications in Computational Physics. 2009.
On a shallow water model for the simulation of turbidity currents [link]Paper   bibtex   abstract  
On some difficulties of the numerical approximation of nonconservative hyperbolic systems. Parés, C.; and Muñoz Ruiz, M. Bol. Soc. Esp. Mat. Apl. 2009.
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On some fast well-balanced first order solvers for nonconservative systems. Díaz, Manuel J., C.; Pardo, A.; Parés, C.; and Toro, E. Math. Comp., 79(271): 1427–1472. 2009.
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. Díaz, Manuel J., C.; González-Vida, J.; Macías, Jorge; and Parés, C. of Numerical Analysis and Applied Mathematics. Realistic application of a tidal 2D two-layer shallow water model to the Strait of Gibraltar, pages 1429-1432. 2009.
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  2008 (9)
Finite volume simulation of the geostrophic adjustment in a rotating shallow-water system. Díaz, Manuel J., C.; López, J.; and Parés, C. SIAM J. Sci. Comput., 31(1): 444–477. 2008.
Finite volume simulation of the geostrophic adjustment in a rotating shallow-water system [link]Paper   bibtex   abstract  
High-order finite volume schemes for shallow water equations with topography and dry areas. Gallardo, J.; Díaz, Manuel J., C.; and Parés, C. 2008.
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Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices. Arregui, I.; Cendán, J. J.; Parés, C.; and Vázquez, C. M2AN Math. Model. Numer. Anal., 42(4): 645–665. 2008.
Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices [link]Paper   bibtex   abstract  
. Díaz, Manuel J., C.; González-Vida, J.; Macías, Jorge; and Parés, C. Simulation of tidal currents in the Strait of Gibraltar. Mofdi, E.; Mohamed, S.; and Naje, Y., editor(s). Universidad Rey Juan Carlos, 2008.
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Simulation of tidal currents in the Strait of Gibraltar using two-dimensional two-layer shallow-water models. Díaz, Manuel J., C.; García-Rodríguez, J.-A.; González-Vida, J.; Macías, Jorge; and Parés, C. Bol. Soc. Esp. Mat. Apl.. 2008.
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Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions. Díaz, Manuel J., C.; García-Rodríguez, J.-A.; González-Vida, J.; and Parés, C. J. Comput. Appl. Math., 221(1): 16–32. 2008.
Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions [link]Paper   bibtex   abstract  
Well-balanced finite volume schemes for 2d non-homogeneous hyperboli systems. Application to the dam break of Aznalcóllar. Díaz, Manuel J., C.; Chacón-Rebollo, T.; Fernández Nieto, E. D.; González-Vida, J.; and Parés, C. Comput. Methods Appl. Mech. Engrg., 197(45-48): 3932–3950. 2008.
Well-balanced finite volume schemes for 2d non-homogeneous hyperboli systems. Application to the dam break of Aznalcóllar [link]Paper   bibtex   abstract  
Well-balanced high order extensions of Godunov's method for semilinear balance laws. Díaz, Manuel J., C.; Gallardo, J.; López-García, Juan-A.; and Parés, C. SIAM J. Numer. Anal., 46(2): 1012–1039. 2008.
Well-balanced high order extensions of Godunov's method for semilinear balance laws [link]Paper   bibtex   abstract  
Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes. Díaz, Manuel J., C.; LeFloch, P.; Muñoz Ruiz, M.; and Parés, C. J. Comput. Phys., 227(17): 8107–8129. 2008.
Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes [link]Paper   bibtex   abstract  
  2007 (5)
Godunov method for nonconservative hyperbolic systems. Muñoz Ruiz, M.; and Parés, C. M2AN Math. Model. Numer. Anal., 41(1): 169–185. 2007.
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Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar. Díaz, Manuel J., C.; García-Rodríguez, J.-A.; González-Vida, J.; Macías, Jorge; and Parés, C. Advances in Engineering Software. 2007.
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On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas. Gallardo, J.; Parés, C.; and Díaz, Manuel J., C. J. Comput. Phys., 227(1): 574–601. 2007.
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On well-balanced finite volume methods for nonconservative nonhomogeneous hyperbolic systems. Díaz, Manuel J., C.; Chacón, T.; Fernández-Nieto, E. D.; and Parés, C. SIAM J. Sci. Comput., 29(3): 1093–1126. 2007.
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Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique. Díaz, Manuel J., C.; Pardo, A.; and Parés, C. Math. Models Methods Appl. Sci., 17(12): 2055–2113. 2007.
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  2006 (5)
A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: application to shallow flows. Díaz, Manuel J., C.; García-Rodríguez, J.-A.; González-Vida, J.; and Parés, C. Comput. Methods Appl. Mech. Engrg., 195(19-22): 2788–2815. 2006.
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High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems. Díaz, Manuel J., C.; Gallardo, J.; and Parés, C. Math. Comp., 75(255): 1103–1134. 2006.
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Numerical methods for nonconservative hyperbolic systems: a theoretical framework. Parés, C. SIAM J. Numer. Anal., 44(1): 300–321. 2006.
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Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme. Díaz, Manuel J., C.; González Vida, J. M.; and Parés, C. Math. Models Methods Appl. Sci., 16(6): 897–931. 2006.
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On a well-balanced high-order finite volume scheme for the shallow water equations with bottom topography and dry areas. Gallardo, J.; Díaz, Manuel J., C.; Parés, C.; and González-Vida, J. 2006.
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  2005 (3)
A generalized duality method for solving variational inequalities. Applications to some nonlinear Dirichlet problems. Gallardo, J.; Díaz, Manuel J., C.; and Parés, C. Numer. Math., 100(2): 259–291. 2005.
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Mathematical models for the simulation of environmental flows: from the Strait of Gibraltar to the Aznalcollar disaster. Parés, C.; Macías, Jorge; and Díaz, Manuel J., C. ERCIM News. 2005.
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The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems. Díaz, Manuel J., C.; Ferreiro, A.; García-Rodríguez, J.-A.; González-Vida, J.; Macías, Jorge; Parés, C.; and Vázquez-Cendón, M. E. Math. Comput. Modelling, 42(3-4): 419–439. 2005.
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  2004 (6)
A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions Application to the Strait of Gibraltar. Díaz, Manuel J., C.; Garcia-Rodriguez, J.; Macías, Jorge; Parés, C.; and Vázquez-Cendón, E. Communications in Nonlinear Science and Numerical Simulation, 9(2): 241–249. 2004.
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A two-layer finite volume model for flows through channels with irregular geometry: computation of maximal exchange solutions. Application to the Strait of Gibraltar. Díaz, Manuel J., C.; Macías, Jorge; Parés, C.; García-Rodríguez, Jose A.; and Vázquez-Cendón, E. Commun. Nonlinear Sci. Numer. Simul.. 2004. Recent advances in computational and mathematical methods for science and engineering
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. Macías, Jorge; Parés, C.; and Díaz, Manuel J., C. Numerical simulation in Oceanography. Application to the Alboran Sea and the Strait of Gibraltar. 2004.
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Numerical simulation of two-layer shallow water flows through channels with irregular geometry. Díaz, Manuel J., C.; García-Rodríguez, José-A.; González-Vida, J.; Macías, Jorge; Parés, C.; and Vázquez-Cendón, M. E. J. Comput. Phys.. 2004.
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On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems. Parés, C.; and Díaz, Manuel J., C. Mathematical Modelling and Numerical Analysis. 2004.
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On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems. Parés, C.; and Díaz, Manuel J., C. M2AN Math. Model. Numer. Anal.. 2004.
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  2003 (1)
On an one-dimensional bi-layer shallow-water problem. Muñoz Ruiz, M.; Díaz, Manuel J., C.; and Parés, C. Nonlinear Anal.. 2003.
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  2002 (3)
A Lagrangian finite element algorithm for the numerical solution of one-dimensional shallow water equations. González Vida, J. M.; and Parés, C. Rev. Internac. Métod. Numér. Cálc. Diseñ. Ingr.. 2002.
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Numerical simulation of internal tides in the Strait of Gibraltar. Díaz, Manuel J., C.; González-Vida, J.; Macías, Jorge; Muñoz Ruiz, M.; Parés, C.; García-Rodríguez, J.; and Vázquez-Cendón, E. RACSAM Rev. R. Acad. Cienc. Exactas Fı́s. Nat. Ser. A Mat.. 2002. Mathematics and environment (Spanish) (Paris, 2002)
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On the convergence of the Bermúdez-Moreno algorithm with constant parameters. Parés, C.; Díaz, Manuel J., C.; and Macías, Jorge Numer. Math.. 2002.
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  2001 (3)
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. Díaz, Manuel J., C.; Macías, Jorge; and Parés, C. M2AN Math. Model. Numer. Anal., 35(1): 107–127. 2001.
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An incomplete LU-based family of preconditioners for numerical resolution of a shallow water system using a duality method. Applications. Díaz, Manuel J., C.; Macías, Jorge; and Parés, C. Appl. Math. Lett.. 2001.
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Duality methods with an automatic choice of parameters. Application to shallow water equations in conservative form. Parés, C.; Macías, Jorge; and Díaz, Manuel J., C. Numer. Math.. 2001.
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  1999 (1)
Improvement and generalization of a finite element shallow-water solver to multi-layer systems. Macías, Jorge; Parés, C.; and Díaz, Manuel J., C. Internat. J. Numer. Methods Fluids. 1999.
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  1998 (1)
. Valle, A.; Parés, C.; Macías, Jorge; and Díaz, Manuel J., C. Numerical resolution of a shallow-water system using a duality method. Application to the Alboran Sea. 1998.
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  1996 (1)
. Díaz, Manuel J., C.; Macías, Jorge; and Parés, C. A multilayer shallow water model. Application to the modelling of the Alboran Sea and the Strait of Gibraltar. 1996.
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  1995 (1)
Navier-Stokes equations with imposed pressure and velocity fluxes. Conca, C.; Parés, C.; Pironneau, O.; and Thiriet, M. Internat. J. Numer. Methods Fluids. 1995.
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  1994 (2)
Approximation de la solution des équations d'un modèle de turbulence par une méthode de Lagrange-Galerkin. Parés, C. Rev. Mat. Apl.. 1994.
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Numerical modelling of water mass exchanges through the Strait of Gibraltar. Macías, Jorge; Díaz, Manuel J., C.; and Parés, C. Revista GAIA. 1994.
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