Gómez-Bueno, I.; Boscarino, S.; Castro, M. J.; Parés, C.; Russo, G. Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws. (English) Zbl 1506.65135 Appl. Numer. Math. 184, 18-48 (2023). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65M06 65N06 65L06 76B15 76M12 76M20 PDFBibTeX XMLCite \textit{I. Gómez-Bueno} et al., Appl. Numer. Math. 184, 18--48 (2023; Zbl 1506.65135) Full Text: DOI arXiv
Aïssiouene, Nora; Bristeau, Marie-Odile; Godlewski, Edwige; Mangeney, Anne; Parés Madroñal, Carlos; Sainte-Marie, Jacques A two-dimensional method for a family of dispersive shallow water models. (English) Zbl 1452.65221 SMAI J. Comput. Math. 6, 187-226 (2020). Reviewer: Marius Ghergu (Dublin) MSC: 65M60 65M08 65M12 76M10 76M12 35L65 35A15 35Q30 35Q35 76B15 76D05 86A15 35R35 PDFBibTeX XMLCite \textit{N. Aïssiouene} et al., SMAI J. Comput. Math. 6, 187--226 (2020; Zbl 1452.65221) Full Text: DOI
Castro, Manuel J.; Parés, Carlos Well-balanced high-order finite volume methods for systems of balance laws. (English) Zbl 1440.65109 J. Sci. Comput. 82, No. 2, Paper No. 48, 48 p. (2020). MSC: 65M08 76M12 76N06 76B15 35Q31 35D30 PDFBibTeX XMLCite \textit{M. J. Castro} and \textit{C. Parés}, J. Sci. Comput. 82, No. 2, Paper No. 48, 48 p. (2020; Zbl 1440.65109) Full Text: DOI
Parés, Carlos; Pimentel, Ernesto The Riemann problem for the shallow water equations with discontinuous topography: the wet-dry case. (English) Zbl 1416.76025 J. Comput. Phys. 378, 344-365 (2019). MSC: 76B15 76B03 65M08 35Q35 PDFBibTeX XMLCite \textit{C. Parés} and \textit{E. Pimentel}, J. Comput. Phys. 378, 344--365 (2019; Zbl 1416.76025) Full Text: DOI
Castro, Manuel J.; La Asunción, Marc De; Fernández Nieto, Enrique D.; Gallardo, José M.; Vida, José M. González; Macías, Jorge; Morales, Tomás; Ortega, Sergio; Parés, Carlos A review on high order well-balanced path-conservative finite volume schemes for geophysical flows. (English) Zbl 1450.65095 Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume IV. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 3515-3539 (2018). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65Y05 65Y10 86A05 86A15 76B15 35Q86 PDFBibTeX XMLCite \textit{M. J. Castro} et al., in: Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1--9, 2018. Volume IV. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 3515--3539 (2018; Zbl 1450.65095) Full Text: DOI
Morales de Luna, Tomás; Castro Díaz, Manuel J.; Parés, Carlos Relation between PVM schemes and simple Riemann solvers. (English) Zbl 1297.65102 Numer. Methods Partial Differ. Equations 30, No. 4, 1315-1341 (2014). Reviewer: Qin Meng Zhao (Beijing) MSC: 65M08 35L65 76L05 35L67 76B15 76M12 PDFBibTeX XMLCite \textit{T. Morales de Luna} et al., Numer. Methods Partial Differ. Equations 30, No. 4, 1315--1341 (2014; Zbl 1297.65102) Full Text: DOI
Morales de Luna, T.; Castro Díaz, M. J.; Parés, C. Reliability of first order numerical schemes for solving shallow water system over abrupt topography. (English) Zbl 1290.76089 Appl. Math. Comput. 219, No. 17, 9012-9032 (2013). MSC: 76M12 65M08 76B15 PDFBibTeX XMLCite \textit{T. Morales de Luna} et al., Appl. Math. Comput. 219, No. 17, 9012--9032 (2013; Zbl 1290.76089) Full Text: DOI arXiv
Castro, Manuel J.; Fjordholm, Ulrik S.; Mishra, Siddhartha; Parés, Carlos Entropy conservative and entropy stable schemes for nonconservative hyperbolic systems. (English) Zbl 1317.65167 SIAM J. Numer. Anal. 51, No. 3, 1371-1391 (2013). Reviewer: Snezhana Gocheva-Ilieva (Plovdiv) MSC: 65M06 65M12 35L72 35Q53 76M20 76B15 PDFBibTeX XMLCite \textit{M. J. Castro} et al., SIAM J. Numer. Anal. 51, No. 3, 1371--1391 (2013; Zbl 1317.65167) Full Text: DOI Link
Castro Díaz, Manuel Jesús; Fernández Nieto, Enrique Domingo; Morales de Luna, Tomás; Narbona-Reina, Gladys; Parés, Carlos A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport. (English) Zbl 1268.76037 ESAIM, Math. Model. Numer. Anal. 47, No. 1, 1-32 (2013). MSC: 76M12 76M20 76N99 65M06 76B15 PDFBibTeX XMLCite \textit{M. J. Castro Díaz} et al., ESAIM, Math. Model. Numer. Anal. 47, No. 1, 1--32 (2013; Zbl 1268.76037) Full Text: DOI
Morales de Luna, T.; Castro Díaz, M. J.; Parés Madroñal, C. A duality method for sediment transport based on a modified Meyer-Peter & Müller model. (English) Zbl 1426.76408 J. Sci. Comput. 48, No. 1-3, 258-273 (2011). MSC: 76M12 76B15 86A05 PDFBibTeX XMLCite \textit{T. Morales de Luna} et al., J. Sci. Comput. 48, No. 1--3, 258--273 (2011; Zbl 1426.76408) Full Text: DOI
Fernández-Nieto, E. D.; Castro Díaz, M. J.; Parés, C. On an intermediate field capturing Riemann solver based on a parabolic viscosity matrix for the two-layer shallow water system. (English) Zbl 1421.76163 J. Sci. Comput. 48, No. 1-3, 117-140 (2011). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{E. D. Fernández-Nieto} et al., J. Sci. Comput. 48, No. 1--3, 117--140 (2011; Zbl 1421.76163) Full Text: DOI Link
Castro-Díaz, M. J.; Fernández-Nieto, E. D.; González-Vida, J. M.; Parés-Madroñal, C. Numerical treatment of the loss of hyperbolicity of the two-layer shallow-water system. (English) Zbl 1416.76140 J. Sci. Comput. 48, No. 1-3, 16-40 (2011). MSC: 76M12 76B55 76B15 PDFBibTeX XMLCite \textit{M. J. Castro-Díaz} et al., J. Sci. Comput. 48, No. 1--3, 16--40 (2011; Zbl 1416.76140) Full Text: DOI Link
Castro, Manuel J.; Pardo, Alberto; Parés, Carlos; Toro, E. F. On some fast well-balanced first order solvers for nonconservative systems. (English) Zbl 1369.65107 Math. Comput. 79, No. 271, 1427-1472 (2010). MSC: 65M08 35L60 76B15 76M20 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Math. Comput. 79, No. 271, 1427--1472 (2010; Zbl 1369.65107) Full Text: DOI
Parés, Carlos Path-conservative numerical methods for nonconservative hyperbolic systems. (English) Zbl 1266.65148 Puppo, Gabriella (ed.) et al., Numerical methods for balance laws. Caserta: Dipartimento di Matematica, Seconda Università di Napoli (ISBN 978-88-548-3360-9/hbk). Quaderni di Matematica 24, 67-121 (2009). MSC: 65M06 65M12 35L65 76B15 76L05 76M20 PDFBibTeX XMLCite \textit{C. Parés}, Quad. Mat. 24, 67--121 (2009; Zbl 1266.65148)
Gallardo, José M.; Castro, Manuel J.; Parés, Carlos High-order finite volume schemes for shallow water equations with topography and dry areas. (English) Zbl 1404.76173 Tadmor, Eitan (ed.) et al., Hyperbolic problems. Theory, numerics and applications. Contributed talks. Proceedings of the 12th international conference on hyperbolic problems, June 9–13, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4730-5/hbk; 978-0-8218-4728-2/2-vol.set). Proceedings of Symposia in Applied Mathematics 67, Part 2, 585-594 (2009). MSC: 76M12 76B15 65M06 35L65 PDFBibTeX XMLCite \textit{J. M. Gallardo} et al., Proc. Symp. Appl. Math. 67, 585--594 (2009; Zbl 1404.76173) Full Text: DOI
González-Vida, José Manuel; Castro-Díaz, Manuel Jesús; García-Rodríguez, José Antonio; Macías Sánchez, Jorge; Parés, Carlos Simulation of tidal currents in the strait of gibraltar using two-dimensional two-layer shallow-water models. (Spanish) Zbl 1242.76235 Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 42, 137-146 (2008). MSC: 76M25 86A05 65M60 76B15 76B55 PDFBibTeX XMLCite \textit{J. M. González-Vida} et al., Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 42, 137--146 (2008; Zbl 1242.76235)
Castro Díaz, M. J.; Chacón Rebollo, T.; Fernández-Nieto, E. D.; González Vida, J. M.; Parés, C. Well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. Application to the dam break of Aznalcóllar. (English) Zbl 1194.76150 Comput. Methods Appl. Mech. Eng. 197, No. 45-48, 3932-3950 (2008). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{M. J. Castro Díaz} et al., Comput. Methods Appl. Mech. Eng. 197, No. 45--48, 3932--3950 (2008; Zbl 1194.76150) Full Text: DOI Link
Castro, M. J.; Férnandez Nieto, E. D.; Ferreiro Ferreiro, A. M.; García Rodríguez, J. A.; Parés, C. High order two dimensional numerical schemes for the coupling of transport equations and shallow water equations. (English) Zbl 1391.65162 Kunisch, Karl (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69776-3/hbk). 241-248 (2008). MSC: 65M08 76B15 76M12 76T20 PDFBibTeX XMLCite \textit{M. J. Castro} et al., in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10--14, 2007. Berlin: Springer. 241--248 (2008; Zbl 1391.65162) Full Text: DOI
Castro, M. J.; García-Rodríguez, J. A.; González-Vida, J. M.; Parés, C. Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions. (English) Zbl 1211.76074 J. Comput. Appl. Math. 221, No. 1, 16-32 (2008). MSC: 76M12 65M06 76B15 65Y10 PDFBibTeX XMLCite \textit{M. J. Castro} et al., J. Comput. Appl. Math. 221, No. 1, 16--32 (2008; Zbl 1211.76074) Full Text: DOI
Gallardo, J. M.; Castro, M.; Parés, C.; González-Vida, J. M. On a well-balanced high-order finite volume scheme for the shallow water equations with bottom topography and dry areas. (English) Zbl 1388.76175 Benzoni-Gavage, Sylvie (ed.) et al., Hyperbolic problems. Theory, numerics and applications. Proceedings of the 11th international conference on hyperbolic problems, Ecole Normale Supérieure, Lyon, France, July 17–21, 2006. Berlin: Springer (ISBN 978-3-540-75711-5/hbk). 259-270 (2008). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{J. M. Gallardo} et al., in: Hyperbolic problems. Theory, numerics and applications. Proceedings of the 11th international conference on hyperbolic problems, Ecole Normale Supérieure, Lyon, France, July 17--21, 2006. Berlin: Springer. 259--270 (2008; Zbl 1388.76175)
Castro Díaz, M. J.; Chacón Rebollo, T.; Fernández-Nieto, E. D.; Parés, Carlos On well-balanced finite volume methods for nonconservative nonhomogeneous hyperbolic systems. (English) Zbl 1148.65065 SIAM J. Sci. Comput. 29, No. 3, 1093-1126 (2007). Reviewer: Weizhong Dai (Ruston) MSC: 65M06 76M12 35L70 76B15 PDFBibTeX XMLCite \textit{M. J. Castro Díaz} et al., SIAM J. Sci. Comput. 29, No. 3, 1093--1126 (2007; Zbl 1148.65065) Full Text: DOI
Castro, Manuel J.; Milanés, Alberto Pardo; Parés, Carlos Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique. (English) Zbl 1137.76038 Math. Models Methods Appl. Sci. 17, No. 12, 2055-2113 (2007). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Math. Models Methods Appl. Sci. 17, No. 12, 2055--2113 (2007; Zbl 1137.76038) Full Text: DOI
Gallardo, José M.; Parés, Carlos; Castro, Manuel On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas. (English) Zbl 1126.76036 J. Comput. Phys. 227, No. 1, 574-601 (2007). MSC: 76M12 76B15 86A05 PDFBibTeX XMLCite \textit{J. M. Gallardo} et al., J. Comput. Phys. 227, No. 1, 574--601 (2007; Zbl 1126.76036) Full Text: DOI
Castro, Manuel J.; García-Rodríguez, José A.; González-Vida, José M.; Macías, Jorge; Parés, Carlos Improved FVM for two-layer shallow-water models: application to the strait of Gibraltar. (English) Zbl 1137.76320 Adv. Eng. Softw. 38, No. 6, 386-398 (2007). MSC: 76B07 76B15 76B55 76M20 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Adv. Eng. Softw. 38, No. 6, 386--398 (2007; Zbl 1137.76320) Full Text: DOI
Castro, M. J.; García-Rodríguez, J. A.; González-Vida, J. M.; Parés, C. A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: application to shallow flows. (English) Zbl 1388.76169 Comput. Methods Appl. Mech. Eng. 195, No. 19-22, 2788-2815 (2006). MSC: 76M12 76B15 65Y05 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Comput. Methods Appl. Mech. Eng. 195, No. 19--22, 2788--2815 (2006; Zbl 1388.76169) Full Text: DOI
Castro, M. J.; García, J. A.; González, J. M.; Parés, C. Computational time improvement for some shallow water finite volume models applying parallelization and optimized small matrix computations. (English) Zbl 1323.76052 Bermúdez de Castro, Alfredo (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18–22, 2005. Berlin: Springer (ISBN 3-540-34287-7/hbk). 288-296 (2006). MSC: 76M12 76B15 65Y05 PDFBibTeX XMLCite \textit{M. J. Castro} et al., in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18--22, 2005. Berlin: Springer. 288--296 (2006; Zbl 1323.76052)
Castro, Manuel J.; González-Vida, José M.; Parés, Carlos Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme. (English) Zbl 1136.65330 Math. Models Methods Appl. Sci. 16, No. 6, 897-931 (2006). MSC: 65M06 35L65 76M12 76B15 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Math. Models Methods Appl. Sci. 16, No. 6, 897--931 (2006; Zbl 1136.65330) Full Text: DOI
Castro, Manuel; Gallardo, José M.; Parés, Carlos High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems. (English) Zbl 1096.65082 Math. Comput. 75, No. 255, 1103-1134 (2006). Reviewer: Song Jiang (Beijing) MSC: 65M06 76M12 35L65 76B15 65M15 PDFBibTeX XMLCite \textit{M. Castro} et al., Math. Comput. 75, No. 255, 1103--1134 (2006; Zbl 1096.65082) Full Text: DOI
Castro, M. J.; Ferreiro Ferreiro, A. M.; García-Rodríguez, J. A.; González-Vida, J. M.; Macías, J.; Parés, C.; Vázquez-Cendón, M. Elena The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems. (English) Zbl 1121.76008 Math. Comput. Modelling 42, No. 3-4, 419-439 (2005). MSC: 76B07 76B15 76B55 76M20 65M06 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Math. Comput. Modelling 42, No. 3--4, 419--439 (2005; Zbl 1121.76008) Full Text: DOI
Castro Díaz, Manuel; Carcía Rodriguez, José A.; González Vida, José M.; Parés Madroñal, Carlos Numerical solution of two-layer shallow water equations using finite volume schemes. (Resolución numérica de las ecuaciones de aguas someras bicapa mediante esquemas de volúmenes finitos.) (Spanish) Zbl 1168.86301 Bernadou, Michel (ed.) et al., Apuntes de la XI escuela Jacques-Louis Lions Hispano-Francesa sobre simulación numérica en física e ingeniería. Cádiz: Grupo de Análisis Teórico y Numérico de Modelos de las Ciencias Experimentales de la Universidad de Cádiz (ISBN 84-688-7650-X/pbk). 199-216 (2004). MSC: 86A05 65M06 76B15 76M12 PDFBibTeX XMLCite \textit{M. Castro Díaz} et al., in: Apuntes de la XI escuela Jacques-Louis Lions Hispano-Francesa sobre simulación numérica en física e ingeniería. Cádiz: Grupo de Análisis Teórico y Numérico de Modelos de las Ciencias Experimentales de la Universidad de Cádiz. 199--216 (2004; Zbl 1168.86301)
Castro, Manuel J.; Macías, Jorge; Parés, Carlos; García-Rodríguez, Jose A.; Vázquez-Cendón, Elena A two-layer finite volume model for flows through channels with irregular geometry: computation of maximal exchange solutions. Application to the Strait of Gibraltar. (English) Zbl 1136.76394 Commun. Nonlinear Sci. Numer. Simul. 9, No. 2, 241-249 (2004). MSC: 76M12 76B15 35L55 76T99 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Commun. Nonlinear Sci. Numer. Simul. 9, No. 2, 241--249 (2004; Zbl 1136.76394) Full Text: DOI
Castro, Manuel J.; García-Rodríguez, Jose A.; Macías, Jorge; Parés, Carlos; Vázquez-Cendón, M. Elena A two-layer numerical model for flows through channels with irregular geometry: application to the water exchange through the Strait of Gibraltar. (English) Zbl 1177.76280 Herbin, Raphaéle (ed.) et al., Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24–28, 2002. London: Hermes Penton Science (ISBN 1-9039-9634-1/pbk). 471-478 (2002). MSC: 76M25 76B15 86A05 PDFBibTeX XMLCite \textit{M. J. Castro} et al., in: Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24--28, 2002. London: Hermes Penton Science. 471--478 (2002; Zbl 1177.76280)
González-Vida, José Manuel; Parés, Carlos A Lagrangian finite element algorithm for the numerical resolution of monodimensional shallow water equations. (Spanish. English summary) Zbl 1101.76359 Rev. Int. Métod. Numér. Cálc. Diseño Ing. 18, No. 3, 385-400 (2002). MSC: 76M10 76B15 65M60 65M50 PDFBibTeX XMLCite \textit{J. M. González-Vida} and \textit{C. Parés}, Rev. Int. Métod. Numér. Cálc. Diseño Ing. 18, No. 3, 385--400 (2002; Zbl 1101.76359)
Parés, Carlos; Macías, Jorge; Castro, Manuel Duality methods with an automatic choice of parameters. Application to shallow water equations in conservative form. (English) Zbl 0991.65057 Numer. Math. 89, No. 1, 161-189 (2001). Reviewer: L.Gasiński (Kraków) MSC: 65K10 49M29 49J40 76B15 76M30 PDFBibTeX XMLCite \textit{C. Parés} et al., Numer. Math. 89, No. 1, 161--189 (2001; Zbl 0991.65057) Full Text: DOI
Castro, M.; Macías, J.; Parés, C. An incomplete LU-based family of preconditioners for numerical resolution of a shallow water system using a duality method—applications. (English) Zbl 1012.76044 Appl. Math. Lett. 14, No. 5, 651-656 (2001). MSC: 76M10 76B15 65M25 PDFBibTeX XMLCite \textit{M. Castro} et al., Appl. Math. Lett. 14, No. 5, 651--656 (2001; Zbl 1012.76044) Full Text: DOI
Macías, Jorge; Pares, Carlos; Castro, Manuel J. Improvement and generalization of a finite element shallow-water solver to multi-layer systems. (English) Zbl 0969.76045 Int. J. Numer. Methods Fluids 31, No. 7, 1037-1059 (1999). MSC: 76M10 76B15 86A05 76B70 76U05 PDFBibTeX XMLCite \textit{J. Macías} et al., Int. J. Numer. Methods Fluids 31, No. 7, 1037--1059 (1999; Zbl 0969.76045) Full Text: DOI
Parés, C.; Castro, M. J.; Macías, J. Numerical resolution of shallow water equations by duality methods with automatic choice of parameters. (Spanish) Zbl 0947.76564 Proceedings of the 15th congress on differential equations and applications and congress on applied mathematics, Vigo, Spain, September 23-26, 1997. Vols. I and II. Vigo: Servicio de Publicacións da Universidade de Vigo. Colecc. Congr. 9, 69-77 (1998). MSC: 76M30 76M10 76B15 65M25 PDFBibTeX XMLCite \textit{C. Parés} et al., in: XV Congreso de ecuaciones diferenciales y aplicaciones y congreso de matemática aplicada, Vigo, España, 23--26 Septiembre 1997. Volumen I e II. Vigo: Servicio de Publicacións da Universidade de Vigo. 69--77 (1998; Zbl 0947.76564)