Research papers

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Macías, J., Escalante, C., Castro, M.J. (2020). Multilayer-HySEA model validation for landslide generated tsunamis. Part I Rigid slides. Under review NHESS.

Macías, J., Escalante, C., Castro, M.J. (2020). Multilayer-HySEA model validation for landslide generated tsunamis. Part II Granular slides. Under review NHESS

Macías, J., Castro, M.J., Escalante, C. (2020).  Performance assessment of Tsunami-HySEA model for NTHMP tsunami currents benchmarking. Laboratory data. Coastal Engineering, 158, 103667, ISSN 0378-3839, [doi: 10.1016/j.coastaleng.2020.103667].

Macías, J., Castro, M.J. Ortega, S., and González-Vida, J.M., (2020).  Performance assessment of Tsunami-HySEA model for NTHMP tsunami currents benchmarking. Field cases. Ocean Modeling, 152, 101645, ISSN 1463-5003, [doi: 10.1016/j.ocemod.2020.101645].

A.M. Ferreiro-Ferreiro, J.A. García-Rodríguez, J.G. López-Salas, C. Escalante, M.J. Castro (2020). Global optimization for data assimilation in landslide tsunami models. Aceptado en Journal of Computational Physics.

T. Morales de Luna, M.J. Castro, C. Chalons (2020). High-order fully well-balanced Lagrange-Projection scheme for shallow water. Aceptado en  Communications in Mathematical Sciences.

J.M. Gallardo, K. A. Schneider, M. J. Castro (2020). On a class of genuinely 2d incomplete Riemann solvers for hyperbolic systems. Aceptado en Computational and Mathematical Methods.

L. Banjai, M. López-Fernández (2019). Numerical approximation of the Schrödinger equation with concentrated potential. Aceptado en Journal of Computational Physics.


Lario, J., Spencer, C., Bardají, T., Marchante, A., Garduño-Monroy, V.H., Macías, J., and Ortega, S. (2019) An extreme wave event in eastern Yucatán, Mexico: Evidence of a paleotsunami event during the Mayan times. Sedimentology, 2019. [].

González-Vida, J.M., Macías, J., Castro, M.J., Sánchez-Linares, C., de la Asunción, M., Ortega, S., and Arcas, D. (2019).  The Lituya Bay landslide-generated mega-tsunami. Numerical simulation and sensitivity analysis,  Natural Hazards and Earth System Science , 19, 369-388 [doi: 10.5194/nhess-19-369-2019]. 

J.M. Gallardo, K. A. Schneider, and M. J. Castro. On a class of two-dimensional incomplete Riemann solvers. Journal of Computational Physics, 386: 541-567, 2019.

C. Escalante, M. Dumbser, and M.J. Castro (2019). An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes. Journal of Computational Physics, 394: 385-416.

M. J. Castro, A. Kurganov, and T. Morales de Luna (2019). Path-conservative central-upwind schemes for nonconservative hyperbolic systems. ESAIM: M2AN, 53 (3): 959-985.

C. Escalante, E. D. Fernández-Nieto,T. Morales de Luna, and M.J. Castro. An Efficient Two-Layer Non-hydrostatic Approach for Dispersive Water Waves. J. Sci. Comput., 79: 273-320, 2019.

M.J. Castro and M. Semplice (2019). Third‐ and fourth‐order well‐balanced schemes for the shallow water equations based on the CWENO reconstruction. Int. J. Numer. Meth. Fluids, 89(8): 304-325. 

C. Parés and E. Pimentel (2019). The Riemann problem for the shallow water equations with discontinuous topography: The wet–dry case. Journal of Computational Physics, 378, 344-365.

H. Carrillo and C. Parés (2019). Compact Approximate Taylor Methods for Systems of Conservation Laws. Journal of Scientific Computing, 80(3): 1832-1866.

L. Banjai, M. López-Fernández (2019). Efficient high order algorithms for fractional integrals and fractional differential equations. Numerische Mathematik, 141(2): 289-317.


López-Venegas, A. M., Chacón-Barrantes, S.E., Zamora, N., and Macías, J. (2018), Nations work together to size up Caribbean tsunami hazards, Eos, 99,[doi: 10.1029/2018EO105609]. Published on 04 October 2018.

Llorente, M. and Macías, J. (2018). La necesidad y la oportunidad de estudiar el impacto económico de los tsunamis en las costas españolas, Revista Digital del Consorcio de Seguros, 9, Autum 2018, 18 pp. [Link].

Llorente, M. and Macías, J. (2018). The need and the oportunity to study the economic impact of tsunamis on Spanish coasts. Revista Digital del Consorcio de Seguros, 9, Autum 2018, 18 pp. [Link].

Hiltebrand, A., Mishra, S., and Parés, C. (2018). Entropy-stable space-time DG schemes for a non-conservative hyperbolic systems. ESAIM Math. Mod. Num. Anal., 52, 995-1022.

Escalante, C., Fernández-Nieto, E.D., Morales, T., and Castro, M.J. (2018). An efficient two-layer non-hydrostatic appproach for dispersive water waves.Journal of Scientific Computing, [doi: 10.1007/s10915-018-0849-9].  


Macías, J., Castro, M.J., Ortega, S., Escalante, C., González-Vida, J.M. (2017). Performance benchmarking of Tsunami-HySEA model for NTHMP's inundation mapping activities. Pure and Applied Geophysics , 1-37.  [doi: 10.1007/s00024-017-1583-1]

Lobo, F.J., Bárcenas, P., Mendes, I., Ortega-Sánchez, M., Macías, J., and Fernández-Salas, L.M. (2017). "Prodeltaic undulations and hyperpycnal flows (II): Evolutionary trends". J. Guillén, J. Acosta, S. Brené, F. Chiocci and A. Palanques eds. Springer. pp. 113-120. [doi: 10.1007/978-3-319-33940-5_19].

Bárcenas, P., Lobo, F.J., Fernández-Salas, L.M., Ortega-Sánchez, M., Mendes, I., and Macías, J. (2017). "Prodeltaic undulations and hyperpycnal flows (I): Morphological observations". J. Guillén, J. Acosta, S. Brené, F. Chiocci and A. Palanques eds. Springer. pp. 107-112.   [doi: 10.1007/978-3-319-33940-5_19].

Lynett, P.J. et al. (2017). Inter-model analysis of tsunami-induced coastal currents. Ocean Modeling,  114:14-32. [More] [doi: 10.1016/j.ocemod.2017.04.003]


Macías, J., Mercado, A., González-Vida, J.M., Ortega, S., and Castro, M.J. (2016). Comparison and numerical performance of Tsunami-HySEA and MOST models for LANTEX 2013 scenario. Impact assessment on Puerto Rico coasts. Pure and Applied Geophysics, 173(12), 3973–3997. [doi:10.1007/s00024-016-1387-8].

Molinari, I., Tonini, R., Piatanessi, A., Lorito, S., Romano, F., Melini, D., González-Vida, J.M., Macías, J., Castro, M.J., and de la Asunción, M. (2016). Fast evaluation of tsunami scenarios: uncertainty assessment for a Mediterranean Sea database. Natural Hazards and Earth Systems Sciences, 16:2593-2602, [doi:10.5194/nhess-16-2593-2016].

Sánchez-Linares, C., Castro, M.J., de la Asunción, M., González-Vida, J.M., Macías, J., and Mishra, S. (2016). Uncertainty quantification in tsunami modeling using Monte-Carlo finite volume method. Journal of Mathematics in Industry, 6:5, 26pp, [doi: 10.1186/s13362-016-0022-8]

Fernández-Nieto, E.D., Morales, T., Narbona-Reina, G., and Zabsonré, J. (2016). "Formal deduction of the Saint-Venant-Exner model including arbitrarily sloping sediment beds and associated energy", ESAIM: Mathematical Modelling and Numerical Analysis.    

Castro, M.J., Gallardo, J.M., and Marquina, A. (2016). "Approximate Osher-Solomon schemes for hyperbolic systems", Applied Mathematics and Computation, Vol. 272, pp. 347-368. 


Macías, J., Vázquez, J.T., Fernández-Salas, L.M., González-Vida, J.M., Bárcenas, P., Castro, M.J., Díaz del Río, V., and Alonso, B. (2015). The Al-Boraní submarine landslide and associated tsunami. A modelling approach. Marine Geology, 361:79-95. [doi:10.1016/j.margeo.2014.12.006].

Lobo, F. J., Goff, J. A., Mendes, I., Bárcenas, P., Fernández-Salas, L. M., Martín-Rosales, W., Macías, J., and Díaz del Río, V. (2015). Spatial variability of prodeltaic undulations on the Guadalfeo River prodelta: support to the genetic interpretation as hyperpycnal flow deposits. Marine Geophysical Research36(4), 309-333. [doi: 10.1007/s11001-014-9233-9 ].

Bárcenas, P., Lobo, F.J., Macías, J., Fernández-Salas, L.M., López-González, N., and Díaz del Río, V. (2015) "Submarine deltaic geometries linked to steep, mountainous drainage basins in the northern shelf of the Alboran Sea: Filling the gaps in the spectrum of deltaic deposition", Geomorphology, Vol. 232, pp. 125-144.   [doi:10.​1016/​j.​geomorph.​2014.​11.​028 ].

Berthon, C., Foucher, F., and Morales, T. (2015). "An efficient splitting technique for two-layer shallow-water model", Numerical Methods for Partial Differential Equations.


Ramírez-Romero, E., Vichi, M., Castro, M.J., Macías, J., Macías, D., García, C.M., and Bruno, M. (2014).  "Modeling biogeochemical seasonal cycle in the Strait of Gibraltar", Journal of Marine Systems, Vol. 139, pp. 348–361. [doi: 10.1016/j.jmarsys.2014.07.017]  

Fernández-Nieto, E. D., Gallardo, J.M., and Vigneaux, P. (2014). "Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case", Journal of Computational Physics, Vol. 264, pp. 55-90.   

Morales, T., Castro, M.J. and Parés, C. (2014). "Relation between PVM schemes and simple Riemann solvers", Numerical Methods for Partial Differential Equations, Vol. 30(4), pp. 1315-1341.  [Online version]  

Moros, J., Serrano, J., Sánchez-Linares, C., Macías, J., and Laserna, J.J. (2014). "Advanced Recognition of Explosives in Traces on Polymer Surfaces Using LIBS and Supervised Learning Classifiers", Analytica Chimica Acta, Vol. 806, pp. 107-116.   [doi: 10.1016/j.aca.2013.11.035]. 

Fernández-Nieto, E. D., Lucas, C., Morales, T., and Cordier, S. (2014). "On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems", Computers & Fluids, Vol. 91, pp. 87-106.  [Online version]  

Castro, M.J., Gallardo, J.M., and Marquina, A. (2014).  "A class of incomplete Riemann solvers based on uniform rational approximations to the absolute value function", Journal of Scientific Computing, Vol. 60. 2014, pp. 363-389.   

Jabaloy, A., Lobo, F.J., Azor, A., Martín-Rosales, W., Pérez-Peña, J.V., Bárcenas, P., Macías, J., Fernández-Salas, L.M., Vázquez-Vílchez, M. (2014). "Six thousand years of coastline evolution in the Guadalfeo deltaic system (southern Iberian Peninsula)", Geomorphology, Vol. 206, pp. 374 - 391.  [doi: 10.1016/j.geomorph.2013.08.037]


Fernández-Nieto, E. D., Koné, E. H., Morales, T., and Bürger, R. (2013). "A multilayer shallow water system for polydisperse sedimentation", Journal of Computational Physics, Vol. 238, pp. 281-314.  [Online version]  

Castro, M.J., López-García, J.A., and Parés, C. (2013). "High order exactly well-balanced numerical methods for shallow water systems", Journal of Computational Physics, Vol. 246, pp. 242 - 264.  [Online version]  

Gallardo, J.M., Fernández-Nieto, E. D. and Vigneaux, P. (2013). "A finite volume/duality method for Bingham viscoplastic flow". Numerical methods for hyperbolic problems: Theory and applications. E. Vázquez-Cendón, A. Hidalgo, P. García-Navarro and L. Cea eds. pp. 121-126. [More]  

de la Asunción, M., Castro, M.J., Fernández-Nieto, E. D., Mantas, J.M., Ortega-Acosta, S. and González-Vida, J. M. (2013). "Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer shallow water system on structured meshes", Computers & Fluids, Vol. 80, pp. 441-452.  [Online version]  

Morales, T. (2013). "Sediment transport: monitoring, modeling, and management". Khan, A. A, Wu and Weiming eds. Nova Publishers, pp. 239-261. [Online version]  

Moros, J., Serrano, J, Galllego, F., Macías, J., and Laserna, J.J. (2013). "Recognition of explosives fingerprints on objects for courier services using machine learning methods and laser-induced breakdown spectroscopy", TALANTA, Vol. 110, pp. 108-117. [doi: 10.1016/j.talanta.2013.02.026]. 

Morales, T., Castro, M.J. and Parés, C. (2013). "Reliability of first order numerical schemes for solving shallow water system over abrupt topography", Applied Mathematics and Computation, Vol. 219, pp. 9012-9032.  [Full text]


Castro, M.J., de la Asunción, M., Macías, J., Parés, C., Fernández-Nieto, E. D., González-Vida, J. M., and Morales, T. (2012). "IFCP Riemann solver: Application to tsunami modelling using GPUs". E. Vázquez, A. Hidalgo, P. García and L. Cea eds. CRC Press, pp. 237-244. 

de la Asunción, M., Mantas, J.M., Castro, M.J., and Fernández-Nieto, E. D. (2012). "An MPI-CUDA implementation of an improved Roe method for two-layer shallow water systems", Journal of Parallel and Distributed Computing, Vol. 72, pp. 1065-1072.  [Online version]

Vázquez, J., Bárcenas, P., Macías, J., Fernández-Salas, L.M.,  Díaz del Río, V., González-Vida, J. M., Castro, M.J. (2012). "Tsunamis generados por deslizamientos submarinos en el Mar de Alborán: Simulación de un posible tsunami a partir del sistema de movimientos en masa Al-Boraní". Resúmenes extendidos del VIII Congreso Geológico de España. Fernández et al eds. pp. 1761-1764. 

Moros, J., Serrano, J., Sánchez-Linares, C., Macías, J., and Laserna, J.J. (2012). "New chemometrics in laser-induced breakdown spectroscopy for recognizing", Journal of Analytical Atomic Spectrometry.  [Online version]

Castro, M.J., Fernández-Nieto, E. D., Morales, T., Narbona-Reina, G. and Parés, C. (2012) "A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport", ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 47, pp. 1-32.  [Online version]

Macías, J. et al. (2012). Deslizamientos Submarinos y Tsunamis en el Mar de Alborán. Un Ejemplo de Modelización., vol. 6, Avda. del Brasil, 31. 28020 Madrid: Instituto Español de Oceanografía. ISBN: 978-84-95877-25-3. URI:   [Online version]


Muñoz, M.L. and Parés, C. (2011). "On the convergence and well-balanced property of path-conservative numerical schemes for systems of balance laws", Journal of Scientific Computing, Vol. 48, pp. 274-295.  [Online version]

Cordier, S., Morales, T. and Le, M. (2011). "Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help", Advances in Water Resources, Vol. 34, pp. 980-989.  [Online version]

Castro, M.J., S. Ortega Acosta, de la Asunción, M., Mantas, J. M., and Gallardo, J.M. (2011)  . "GPU computing for shallow water flow simulation based on finite volume schemes", Comptes Rendus Mécanique, Vol. 339, pp. 165-184. 

de la Asunción, M., J. M. Mantas and Castro, M.J. (2011). "Simulation of one-layer shallow water systems on multicore and CUDA architectures", The Journal of Supercomputing, Vol. 58, pp. 206-214.  [Online version]

Gallardo, J.M., S. Ortega Acosta, de la Asunción, M., and Mantas, J.M. (2011). "Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs", Journal of Scientific Computing, Vol. 48, pp. 141-163.  [Online version]

Fernández-Nieto, E.D., Castro, M.J. and Parés, C. (2011). "On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System", Journal of Scientific Computing, Vol. 48, pp. 117-140.  [Online version]

Castro, M.J., Fernández-Nieto, E. D., González-Vida, J. M., and Parés, C. (2011). "Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System", Journal of Scientific Computing, Vol. 48, pp. 16-40.  [Online version]

Morales, T., Castro, M.J. and Parés, C. (2011). "A Duality Method for Sediment Transport Based on a Modified Meyer-Peter & Müller Model", Journal of Scientific Computing, Vol. 48, pp. 258-273.  [Online version]

Bárcenas, P., Lobo, F.J., Macías, J., Fernández-Salas, L.M., and Díaz del Río, V. (2011). "Spatial variability of surficial sediments and bakscatter on the northern shelf of the Alboran Sea: The effects of hydrodynamic forcing and local sediment supplies", Journal Iberian Geolology, Vol. 37, pp. 195:214.[doi: 10.5209/rev_JIGE.2011.v37.n2.8].  [Full text]


de la Asunción, M., Mantas, J. M. and Castro, M.J. (2010). "Programming CUDA-Based GPUs to Simulate Two-Layer Shallow Water Flows". P. D’Ambra, M. Guarracino and D. Talia eds. Springer Berlin / Heidelberg. pp. 353-364.  [Online version]  

Castro, M.J., de la Asunción, M., J. M. Mantas and S. Ortega Acosta (2010). "On the benefits of using GPUs to simulate shallow flows with finite volume schemes", Bol. Soc. Esp. Mat. Apl., Vol. 50, pp. 27-44.   

Castro, M.J., Pardo, A., Parés, C., and Toro, E. (2010). "On some fast well-balanced first order solvers for nonconservative systems.", Mathematics of Computation, Vol. 79. 2010, pp. 1427–1472.   

Bárcenas, P., Fernández-Salas, L.M., Macías, J., Lobo, F.J., and Díaz del Río, V. (2010). "Estudio morfométrico comparativo entre las ondulaciones de los prodeltas de los ríos de Andalucía Oriental", Rev. Soc. Geol. España, Vol. 22.  [Full text]  

Bruno, M., Macías, J., González-Vida, J. M., and Vázquez, Á. (2010). "Analysing the tidal-related origin of subinertial flows through the Strait of Gibraltar", J. Geophys. Res. [doi: 10.1029/2010JC006499].   

Bouchut, F. and Morales, T. "A Subsonic well-balanced reconstruction scheme for shallow water flows", SIAM Journal on Numerical Analysis, Vol. 48. 2010, pp. 1733.  [Online version]  

Dumbser, M., Hidalgo, A., Castro, M.J., Parés, C. and Toro, E. F. (2010). "FORCE schemes on unstructured meshes II: Nonconservative hyperbolic systems", Comput. Methods Appl. Mech. Engrg., Vol. 199, pp. 625–647.  [Online version]


Bárcenas, P., Fernández-Salas, L. M., Macías, J., Lobo, F. J., and Díaz del Río, V. (2009). "Estudio morfométrico entre las ondulaciones de los prodeltas de los ríos de Andalucía Oriental". J. A. Morales, M. Cantano, A. Rodríguez-Ramírez, I. Delgado and eds. pp. 13-17. 

Bárcenas, P., Fernández-Salas, L. M., Lobo, F., Macías, J. and Díaz del Río, V. (2009). "Estudio morfométrico de las ondulaciones de los ríos de Andalucía oriental". J. A. Morales, M. Cantano, A. Rodríguez-Ramírez, I. Delgado and eds. pp. 13-17.   

Castro, M.J., González-Vida, J. M., Macías, J., and Parés, C. (2009). "Realistic application of a tidal 2D two-layer shallow water model to the Strait of Gibraltar", pp. 1429-1432.   

Morales, T. (2009). Entropy satisfying schemes for shallow water systems, VDM Verlag.  [Online version]  

Bouchut, F. and Morales, T. (2009). "Semi-discrete Entropy Satisfying Approximate Riemann Solvers. The Case of the Suliciu Relaxation Approximation", Journal of Scientific Computing, Vol. 41, pp. 483-509.  [Online version]  

Parés, C. and Muñoz, M.L. (2009). "On some difficulties of the numerical approximation of nonconservative hyperbolic systems", Bol. Soc. Esp. Mat. Apl.   

Dumbser, M., Castro, M.J., Parés, C., and Toro, E.F. (2009). "ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows", Computers & Fluids, Vol. 38, pp. 1731–1748.  [Online version]  

Castro, M.J., Pardo, A., Parés, C. and Toro, E.F. (2009). "On some fast well-balanced first order solvers for nonconservative systems", Math. Comp., Vol. 79, pp. 1427–1472.   

Lastra, M., Mantas,  J. M., Ureña, C., Castro, M.J., and García, J. A. (2009). "Simulation of shallow-water systems using graphics processing units",  Math. Comp. Simul., 80(3):598 – 618.

Morales, T., Castro, M.J., Parés, C., and Fernández-Nieto, E. D. (2009). "On a shallow water model for the simulation of turbidity currents", Communications in Computational Physics.  [Online version]  

Castro, M.J., Fernández-Nieto, E. D., Ferreiro,  A. M., García-Rodríguez, J. A., and Parés, C. (2009). "High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems", J. Sci. Comput., Vol. 39, pp. 67–114. 


Gallardo, J.M., Castro, M.J. and Parés, C. (2008). "High-order finite volume schemes for shallow water equations with topography and dry areas". Hyperbolic problems: Theory, numerics and applications. E. Tadmor, J.-G. Liu and A. Tzavaras eds. pp. 585-594. 

Castro, M.J.,González-Vida, J. M., Macías, J., and Parés, C. (2008). "Simulation of tidal currents in the Strait of Gibraltar". M. E. Amrani, M. Sead and N. Yebari eds. Universidad Rey Juan Carlos. 

Bouchut, F. and Morales, T. (2008). "An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment", ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN). 2008.  [Online version]

Castro, M.J., Fernández-Nieto, E. D., and Ferreiro, A. (2008). "Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods", Comput Fluids

Morales, T. (2008). "A Saint Venant model for gravity driven shallow water flows with variable density and compressibility effects", Mathematical and Computer Modelling.  [Online version]

Castro, M.J., Gallardo, J.M, López-García, J.A., and Parés, C. (2008). "Well-balanced high order extensions of Godunov's method for semilinear balance laws", SIAM J. Numer. Anal., Vol. 46, pp. 1012–1039.  [Online version]

Castro, M.J., García-Rodríguez, J. A., González-Vida, J. M., Macías, J., and Parés, C. (2008). "Simulation of tidal currents in the Strait of Gibraltar using two-dimensional two-layer shallow-water models", Bol. Soc. Esp. Mat. Apl. 

Fernández-Nieto, E.D., Bouchut, F., Bresch, D., Castro, M.J. and Mangeney, A. (2008). "A new Savage-Hutter type model for submarine avalanches and generated tsunami", J. Comput. Phys. 

Arregui, I., Cendán, J. J., Parés, C. and Vázquez, C. (2008). "Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices", M2AN Math. Model. Numer. Anal., Vol. 42, pp. 645–665.  [Online version]

Castro, M.J., LeFloch, P. G., Muñoz, M.L., and Parés, C. (2008). "Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes", J. Comput. Phys., Vol. 227, pp. 8107–8129.  [Online version]

Castro, M.J., Rebollo, T. C., Fernández-Nieto, E. D., González-Vida, J. M., and Parés, C. (2008). "Well-balanced finite volume schemes for 2d non-homogeneous hyperboli systems. Application to the dam break of Aznalcóllar", Comput. Methods Appl. Mech. Engrg., Vol. 197, pp. 3932–3950. [Online version]

Castro, M.J., García-Rodríguez, J. A., González-Vida, J. M., and Parés, C. (2008). "Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions", J. Comput. Appl. Math., Vol. 221, pp. 16–32.  [Online version]

Castro, M.J., J. A. López and Parés, C. (2008). "Finite volume simulation of the geostrophic adjustment in a rotating shallow-water system", SIAM J. Sci. Comput., Vol. 31, pp. 444–477.  [Online version]


Castro, M.J., García-Rodríguez, J. A., González-Vida, J. M., Macías, J., and Parés, C. (2007). "Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar", Advances in Engineering Software

Castro, M.J., T. Chacón, E. D. Fernández-Nieto and Parés, C. (2007). "On well-balanced finite volume methods for nonconservative nonhomogeneous hyperbolic systems", SIAM J. Sci. Comput., Vol. 29, pp. 1093–1126. 

Muñoz, M.L. and Parés, C. (2007). "Godunov method for nonconservative hyperbolic systems", M2AN Math. Model. Numer. Anal., Vol. 41, pp. 169–185.  

Gallardo, J.M., Parés, C. and Castro, M.J. (2007). "On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas", J. Comput. Phys., Vol. 227, pp. 574–601.   

Castro, M.J., A. Pardo and Parés, C. (2007). "Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique", Math. Models Methods Appl. Sci., Vol. 17, pp. 2055–2113. 


Gallardo, J.M., Castro, M.J., Parés, C. , and González-Vida, J. M. (2006). "On a well-balanced high-order finite volume scheme for the shallow water equations with bottom topography and dry areas". Hyperbolic problems: Theory, numerics and applications. S. Benzoni-Gavage and D. Serre eds. pp. 259-270. 

Castro, M.J., J. A. García-Rodríguez, González-Vida, J. M., and Parés, C. (2006). "A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: application to shallow flows", Comput. Methods Appl. Mech. Engrg., vol. 195, pp. 2788–2815. 

Parés, C. (2006). "Numerical methods for nonconservative hyperbolic systems: a theoretical framework", SIAM J. Numer. Anal., vol. 44, pp. 300–321. 

Castro, M.J., Gallardo, J.M. and Parés, C. (2006). "High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems", Math. Comp., vol. 75, pp. 1103–1134. 

Castro, M.J., González-Vida, J. M., and Parés, C. (2006). "Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme", Math. Models Methods Appl. Sci., vol. 16, pp. 897–931. 


Parés, C. , Castro, M.J. and Gallardo, J.M. (2005). "Métodos numéricos para sistemas hiperbólicos no conservativos. Aplicación a un modelo bicapa de aguas someras". Modelización matemática de la sedimentación en la costa. J. Castelló and V. Martínez eds. pp. 117-140.

Parés, C. , Macías, J. and Castro, M.J. (2005) . "Mathematical models for the simulation of environmental flows: from the Strait of Gibraltar to the Aznalcollar disaster", ERCIM News, vol. 61, pp. 33-34.

Gallardo, J.M., Castro, M.J. and Parés, C. (2005) . "A generalized duality method for solving variational inequalities. Applications to some nonlinear Dirichlet problems", Numer. Math., Vol. 100, pp. 259–291.

Castro, M.J., Ferreiro, A.M., García-Rodríguez, J.A., González-Vida, J. M., Macías, J., Parés, C., and Vázquez-Cendón, M.E. (2005). "The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems", Math. Comput. Modelling, vol. 42, pp. 419–439.


Macías, J., Parés, C. , and Castro, M.J. (2004). "Numerical simulation in Oceanography. Application to the Alboran Sea and the Strait of Gibraltar". Ocean Circulation and Pollution Control - A Mathematical and Numerical Investigation, in J.I. Díaz ed., A Diderot Mathematical Forum. pp. 75-98. Springer Verlag. ISBN: 3-540-40647-6

Castro, M.J., García-Rodríguez, J.A., Macías, J., Parés, C. and Vázquez-Cendón, E. (2004). "A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions Application to the Strait of G,ibraltar", Communications in Nonlinear Science and Numerical Simulation, Vol. 9, pp. 241–249.

Castro, M.J., García-Rodríguez, J.A., González-Vida, J. M., Macías, J., Parés, C., and Vázquez-Cendón, M.E. (2004). "Numerical simulation of two-layer shallow water flows through channels with irregular geometry", J. Comput. Phys., vol. 195, pp. 202-235.

Castro, M.J., Macías, J., Parés, C. , García-Rodríguez, J. A., and Vázquez-Cendón. E. (2004). "A two-layer finite volume model for flows through channels with irregular geometry: computation of maximal exchange solutions. Application to the Strait of Gibraltar", Commun. Nonlinear Sci. Numer. Simul.

Parés, C. and Castro, M.J. (2004) . "On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems", M2AN Math. Model. Numer. Anal.

Muñoz, M.L. (2004). "On a non-homogeneous bi-layer shallow-water problem: an existence theorem", Diff. Int. Eq.

Muñoz, M.L. (2004). "On a non-homogeneous bi-layer shallow-water problem: smoothness and uniqueness results", Nonlinear Anal.

Parés, C. and Castro, M.J. (2004) . "On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems", Mathematical Modelling and Numerical Analysis.

Macías, J. (2004). "Los Niños de los Trópicos": qué son, sus modelos y su predicción", Boletín de la Sociedad Española de Matemática Aplicada, vol. 27, pp. 49-78.


Gallardo, J.M.. (2003) . "Generation of analytic semigroups by differential operators with mixed boundary conditions", Rocky Mountain Journal of Mathematics, Vol. 33, pp. 831-863. 

Macías, J. (2003) . "El fenómeno "El Niño": reseña histórica, modelos y predicciones", Boletín de la Sociedad Malagueña de Ciencias, vol. V, pp. 51-70.

Muñoz, M.L., Chatelon, F. and Orenga, P. (2003) . "On a bi-layer shallow-water problem", Nonlinear Anal. 

Muñoz, M.L., Castro, M.J., and Parés, C. (2003) . "On an one-dimensional bi-layer shallow-water problem", Nonlinear Anal.


Parés, C. , Castro, M.J. and Macías, J. (2002) . "On the convergence of the Bermúdez-Moreno algorithm with constant parameters", Numer. Math., vol. 92(1), pp. 113-128.

González-Vida, J. M., and Parés, C. (2002) . "A Lagrangian finite element algorithm for the numerical solution of one-dimensional shallow water equations", Rev. Internac. Métod. Numér. Cálc. Diseñ. Ingr.

Castro, M.J., González-Vida, J. M., Macías, J., Muñoz, M.L., and Parés, C. , García-Rodríguez, J.A., and Vázquez-Cendón, M.E. (2002). "Numerical simulation of internal tides in the Strait of Gibraltar", RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 96(3), pp. 321-340.


Gallardo, J.M.. (2001). "Differential operators with mixed boundary conditions: generation of analytic semigroups", Nonlinear Analysis: Theory, Methods and Applications, Vol. 47, pp. 1333-1344.

Castro, M.J., Macías, J. and Parés, C. (2001). "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", M2AN Math. Model. Numer. Anal., Vol. 35, pp. 107–127.

Castro, M.J., Macías, J., and Parés, C. (2001). "An incomplete LU-based family of preconditioners for numerical resolution of a shallow water system using a duality method. Applications", Appl. Math. Lett., vol. 14, pp. 651-656.

Castro, M.J. and García-Navarro, P. (2001) . "The application of a conservative grid adaptation technique to 1{D} shallow water equations", Math. Comput. Modelling.

Parés, C. , Macías, J., and Castro, M.J. (2001). "Duality methods with an automatic choice of parameters. {A}pplication to shallow water equations in conservative form", Numer. Math., 89(1), pp. 161-189.

Macías, J. (2001). "Estudio del fenómeno "El Niño" mediante un modelo acoplado híbrido de océano-atmósfera", Rev. Geofís., vol. 54, pp. 5-34.


Gallardo, J.M. (2000). "Second-order differential operators with integral boundary conditions and generation of analytic semigroups", Rocky Mountain Journal of Mathematics, Vol. 30, pp. 1265-1291. 

Gallardo, J.M. (2000). "Generation of analytic semigroups by second-order differential operators with non-separated boundary conditions", Rocky Mountain Journal of Mathematics, Vol. 30, pp. 869-899.

S. Février, Frankignoul, C., Sirven, J., Davey, M.K., Delecluse, P., Ineson, S., Macías, J., Sennéchael, N., and Stephenson, D.B. (2000). "A multivariate intercomparison between three oceanic GCMs using observed current and thermocline depth anomalies in the tropical Pacific during 1985-1992", Journal of Marine Systems, vol. 24, pp. 249-275.  [doi: 10.1016/S0924-7963(99)00089-5]


Macías, J., Parés, C. , and Castro, M.J. (1999). "Improvement and generalization of a finite element shallow-water solver to multi-layer systems", Internat. J. Numer. Methods Fluids, 31, pp. 1037-1059.

Macías, J., Stephenson, D., and Kearsley, A. (1999) "A basic reference state suitable for anomaly coupled ocean-atmosphere climate models", Appl. Math. Lett., Vol. 12(1), pp. 21-24.


Valle, A., Parés, C. , Macías, J., and Castro, M.J. (1998). "Numerical resolution of a shallow-water system using a duality method. Application to the Alboran Sea". Équations aux Dérivées  Partielles et Applications. Articles Dédiés à Jacques-Louis Lions. pp. 759-786. Gauthier-Villars, Elsevier. ISBN:  2-84299-041-2.


Gallardo, J.M. (1997). "Second-order ODE's with non-separated boundary conditions and generation of analytic semigroups", Nonlinear Analysis: Theory, Methods and Applications, Vol. 30, pp. 4991-4994.

Castro, M.J., F. Hecht, Mohammadi, B., and Pironneau, O. (1997). "Anisotropic unstructured mesh adaption for flow simulations", Internat. J. Numer. Methods Fluids

Macías, J. and Stephenson, D. (1997). "Seasonal and interannual ENSO variability in a Hybrid Coupled Model of the tropical Pacific", Comptes Rendus de l'Académie des Sciencies de Paris, série II a, 324(14), pp. 269-276.


Macías, J., D. Stephenson, L. Terray and Belamari, S. (1996). "Interannual variability simulated in the tropical Pacific". The Mathematics of Models for Climatology and Environment, in I. Díaz ed., NATO ASI Series I: Global Environmental Change, vol. 48, pp. 367-394. Springer Verlag. ISBN: 3-540-61879-1

Castro, M.J., Macías, J., and Parés, C . (1996). "A multilayer shallow water model. Application to the modelling of the Alboran Sea and the Strait of Gibraltar". The Mathematics of Models for Climatology and Environment, in I. Díaz ed., NATO ASI Series I: Global Environmental Change, vol. 48, pp. 395-408. Springer Verlag. ISBN: 3-540-61879-1


Conca, C.,  Parés, C. , Pironneau, O., and Thiriet, M. (1995). "Navier-Stokes equations with imposed pressure and velocity fluxes", Internat. J. Numer. Methods Fluids.


Parés, C. (1994). "Approximation de la solution des équations d'un modèle de turbulence par une méthode de Lagrange-Galerkin", Rev. Mat. Apl.

Macías, J., Castro, M.J., and Parés, C. (1994). "Numerical modelling of water mass exchanges through the Strait of Gibraltar", Revista GAIAvol. 9, pp. 35-38.

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