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Carlos María Parés Madroñal

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Selected presentations

Scientific metrics (ISI Web of Knowledge)

  • Articles: 81
  • Sum of the Times Cited: 2236
  • Average Citations per Article: 27,6
  • h-index: 25

Top cited papers

  • C. Parés. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM Jour. Num. Anal., 44, 300-321, 2006. Number citations: 249 (ISI WoK), 404 (Google Scholar).
  • M.J. Castro, J.M. Gallardo, C. Parés. High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow water systems. Math. Comp. 75: 1103-1134, 2006. Number citations: 173 (ISI WoK), 259 (Google Scholar).
  • C. Parés, M.J. Castro. On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems. ESAIM-Math. Model. Num. 38 (5): 821-852, 2004. Number citations: 144 (ISI WoK), 232 (Google Scholar).
  • J.M. Gallardo, C. Parés, M.J. Castro. On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas. J. Comp. Phys. 227, 574-601, 2007. Number citations: 133 (ISI WoK), 198 (Google Scholar).
  • M.J. Castro, P.G. LeFloch, M.L. Muñoz, C. Parés. Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes. J. Comp. Phys. 227, 8107-8129, 2008. Number citations: 131 (ISI WoK), 198 (Google Scholar).
  • M.J. Castro, J. Macías, C. Parés. 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. ESAIM-Math. Model. Num. 35 (1): 107-127, 2001. Number citations: 116 (ISI WoK), 175 (Google Scholar). Back to top

Journal articles:

  1. M.J. Castro, S. Ortega, C. Parés. Well-balanced methods for the Shallow Water equations in spherical coordinates. Submitted.
  2. A. Hiltebrand, S. Mishra, C. Parés. Entropy-stable space-time DG schemes for non-conservative hyperbolic systems. Submitted.
  3. A. Beljadid, P.G LeFloch, S. Mishra, C. Parés. Schemes with well-controlled dissipation. Hyperbolic systems in non-conservative form. Comm. Comp. Phys. 21: 913-946, 2017.
  4. S. Jerez, C. Parés. Entropy Stable Schemes for Degenerate Convection-Diffusion Equations. SIAM J. Num. Anal. 55: 240-264, 2017.
  5. M.J. Castro, T. Morales, C. Parés. Relation between PVM schemes and simple Riemann solvers. Num. Meth. P.D.E. 30: 1315-1341, 2014.
  6. M.J. Castro, T. Morales, C. Parés. Reliability of first order numerical schemes for solving shallow water system over abrupt topography. Appl. Math. Comp. 219: 9012-9032, 2013.
  7. M.J. Castro, E.D. Fernández-Nieto, T. Morales, G. Narbona, C. Parés. A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport. ESAIM: Math. Mod. Num. Anal. 47: 1-23, 2013.
  8. L. Müller, C. Parés, E.F. Toro. Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties. J. Comput. Phys. 242: 53-85, 2013.
  9. M.J. Castro, U. Fjordholm, S. Mishra, C. Parés. Entropy conservative and entropy stable schemes for non-conservative hyperbolic systems. SIAM J. Num. Anal. 51: 1371-1391, 2013.
  10. M.J. Castro, J.A. López, C. Parés. High order exactly well-balanced numerical methods for shallow water systems. J. Comp. Phys 246: 242-264, 2013.
  11. M.J. Castro, C. Parés, G. Puppo, G. Russo. Central schemes for nonconservative systems. SIAM J. Sci. Comput. 34: 532-558, 2012.
  12. M.J. Castro E.D. Fernández-Nieto,J.M. González-Vida, C. Parés. Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System. J. Sci. Comput, 48: 16 40, 2011.
  13. T. Morales de Luna, M.J. Castro, C. Parés. A Duality Method for Sediment Transport Based on a Modified Meyer-Peter & Müller Model. J. Sci. Comput, 48: 258-273, 2011.
  14. E.D Fernández-Nieto, M.J. Castro, C. Parés. On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two- Layer Shallow Water System. J. Sci. Comput, 48: 117-140, 2011.
  15. M.L. Muñoz, C. Parés. On the convergence and well-balanced property of path- conservative numerical schemes for systems of balance laws. J. Sci. Comput. 48: 274-295, 2011.
  16. M. Dumbser, A. Hidalgo, M.J. Castro, C. Parés, E. F. Toro. FORCE schemes on unstructured meshes II: Nonconservative hyperbolic systems. Applications to Geophysical Flows. Comp. Meth. Appl. Mech. Eng., 199: 625-647, 2010.
  17. M. Castro, A. Pardo, C. Parés, E. F. Toro. On some fast well-balanced first order solvers for nonconservative systems. Math. Comp, 79(271): 1427-1472, 2010.
  18. M. J. Castro, E.D. Fernandez-Nieto, A.M. Ferreiro, C. Parés. Two-dimensional Sediment Transport models in Shallow Water equations. A second order finite volume approach on unstructured meshes. Comp. Meth. Appl. Mech. Eng, 198: 2520-2538, 2009.
  19. M. J. Castro, E.D. Fernandez-Nieto, A.M. Ferreiro, J. A. García, C. Parés. High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems. J. Sci. Comput, 39: 67-114, 2009.
  20. T. Morales, M. J. Castro, C. Parés, E.D. Fernandez-Nieto. On a Shallow water model for the simulation of turbidity currents. Commun. Comput. Phys 6(4): 848-882, 2009.
  21. M. Dumbser, M. J. Castro, C. Parés, E. F. Toro. ADER Schemes on Unstructured Meshes for Nonconservative Hyperbolic Systems: Applications to Geophysical Flows. Computers and Fluids, 38: 1731-1748, 2009.
  22. M. Castro, J.M. Gallardo, J.A. López, C. Parés. Well-balanced high order extensions of Godunov's method for semi-linear balance laws. SIAM J. Num. Anal.,46: 1012-1039, 2008.
  23. M.J. Castro, P.G. LeFloch, M.L. Muñoz, C. Parés. Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes. J. Comp. Phys. 227, 8107-8129, 2008.
  24. I. Arregui, J.J. Cendán, C. Vázquez, C. Parés. Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices. ESAIM-Math. Model. Num. 42, 645-665, 2008.
  25. M.J. Castro, J.A. García-Rodríguez, J.M. González-Vida, C. Parés. Solving shallow water systems in 2d domains using finite volume methods and multimedia SSE instructions. J. Comput. App. Math, 221: 16-32, 2008.
  26. M. J. Castro, T. Chacón Rebollo, J.M. González Vida, C. Parés. Well-Balanced Finite Volume schemes for 2D non-homogeneous hyperbolic systems. Application to the Dam-break of Aznalcollar. Comp. Meth. Appl. Mech. Eng, 197: 3932-3950, 2008.
  27. M.J. Castro, J.A. López, C. Parés. Finite volume simulation of the geostrophic adjustment in a rotating shallow water system. SIAM J. Sci. Comput. 31, 444- 447, 2008.
  28. M.J. Castro, A.M. Ferreiro, J.A. García, J.M. González, C. Parés. Two-layer flow model: application to the simulation of spill motions. Houille Blanche - Rév. Int. de l'éau. 5, 85 88, 2007.
  29. M.L. Muñoz, C. Parés. Godunov method for nonconservative hyperbolic systems. ESAIM-Math. Model. Num. 41, 169-185, 2007.
  30. J.M. Gallardo, C. Parés, M. Castro. On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas. J. Comput. Phys. 227: 574 601, 2007.
  31. M.J. Castro, J.A. García-Rodríguez, J.M. González-Vida, J. Macías, C. Parés. Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar. Adv. Eng. Soft. 38(6): 386-398, 2007.
  32. M.J. Castro, A. Pardo, C. Parés . Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique. Math. Mod. Meth. App. Sci. Vol. 17, No. 12, 2055-2113, 2007.
  33. T. Chacón, E.D. Fernández, M.J. Castro, C. Parés. On well-balanced finite volume methods for non-conservative non-homogeneous hyperbolic systems. SIAM J. Sci. Comput. 29(3): 1093-1126, 2007.
  34. M.J. Castro, J.M. Gallardo, C. Parés. High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow water systems. Math. Comp. 75: 1103-1134, 2006.
  35. M.J. Castro, J.A. García, J.M. González, C. Parés. A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: application to shallow flows. Comp. Meth. Appl. Mech. Eng. 196, 2788-2815, 2006.
  36. M.J. Castro, J.M. González, C. Parés. Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme. Math. Mod. Meth. App. Sci. Vol. 16, No. 6, 897-931, 2006.
  37. C. Parés. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM Jour. Num. Anal., 44, 300-321, 2006.
  38. J.M. Gallardo, C. Parés, M.J. Castro. A generalized duality method for solving variational inequalities. Applications to some nonlinear Dirichlet problems. Num. Math. 100 (2): 259 291, 2005.
  39. M.J. Castro, A.M. Ferreiro, J.A. García, J.M. González, J. Macías, C. Parés, M.E. Vázquez. On the numerical treatment of wet/dry fronts in shallow flows: applications to one-layer and two-layer systems. Math. Comp. Model. 42 (3-4): 419-439, 2005.
  40. C. Parés, J. Macías, M.J. Castro. Mathematical models for the simulation of environmental flows: from the Strait of Gibraltar to the Aznalcollar disaster. ERCIM News 61: 33-34, 2005.
  41. C. Parés, M.J. Castro. On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems. ESAIM-Math. Model. Num. 38 (5): 821-852, 2004.
  42. M.J. Castro, J.A. García, J.M. González, J. Macías, C. Parés, M.E. Vázquez. Numerical simulation of two-layer shallow water flows through channels with irregular geometry. J. Comput. Phys. 195 (1): 202-235, 2004.
  43. M.J. Castro, J. Macías, C. Parés, J.A. García, M.E. Vázquez. A two-layer finite volume model for flows through channels with irregular geometry: computation of maximal exchange solutions. Application to the Strait of Gibraltar. Comm. Nonlinear Sci. Num. Simul. 9: 241-249, 2004.
  44. M.L. Muñoz, M.J. Castro, C. Parés. On a one-dimensional bi-layer shallow- water problem. Nonlinear Anal.-Theor. 53 (5): 567-600, 2003.
  45. C. Parés, M.J. Castro, J. Macías. On the convergence of the Bermúdez-Moreno algorithm with constant parameters. Numer. Math. 92 (1): 113-128, 2002.
  46. M.J. Castro, J.M. González, J. Macías, M.L. Muñoz, C. Parés, J.A. García, M.E. Vázquez. Numerical simulation of internal tides in the Strait of Gibraltar. Rev. R. Acad. Cien. Serie A Mat. 96 (3): 321-340, 2002.
  47. C. Parés, J. Macías, M.J. Castro. Duality methods with an automatic choice of parameters. Application to shallow water equations in conservative form. Numer. Math. 89: 161-189, 2001.
  48. M.J. Castro, J. Macías, C. Parés. An incomplete LU-based family of preconditioners for numerical resolution of a shallow water system using a duality method. Applications. Appl. Math. Lett. 14 (5): 651-656, 2001.
  49. M.J. Castro, J. Macías, C. Parés. 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. ESAIM Math. Model. Num. 35 (1): 107-127, 2001.
  50. J. Macías, C. Parés, M.J. Castro. Improvement and generalization of a finite element shallow-water solver to multilayer systems. Int. J. Numer. Meth. Fluids 31 (7): 1037-1059, 1999.
  51. C. Conca, C. Parés, O. Pironneau, M. Thiriet. Navier-Stokes equations with imposed pressure and velocity fluxes. Int. J. Numer. Meth. Fluids. 20, 267-287, 1995.
  52. C. Parés. Approximation de la solution des équations d'un modèle de turbulence par une méthode de Lagrange-Galerkin. Rev. Mat. Apl. 15, 63-124, 1994.
  53. C. Parés. Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids. Applicable Analysis, 43, 245-296, 1992.
  54. M. Thiriet, C. Parés, F. Hecht, E. Saltel. Numerical simulation of steady flow in a model of the aortic bifurcation. J. Biomech. Eng-Trasn. AMSE, 144, 40-49, 1992.
  55. C. Bègue, B. Cardot, C. Parés, O. Pironneau. Simulation of turbulence with transient mean. Int. J. Numer. Meth. Fluids. 11, 677-695, 1990.
  56. C. Parés. Un traitement faible en éléments finis de la condition de glissement sur une paroi pour les équations de Navier-Stokes. C. R. Acad. Scien. Paris, Série I. 307:101-106, 1988. 
  57. M.J. Castro, C. Parés Well-Balanced High-Order Finite Volume Methods for Systems of Balance Laws. J Sci Comput 82, 2020, 48.
  58. N. Aïssiouene, M.-O. Bristeau, E. Godlewski, A. Mangeney, C. Parés, J. Sainte-Marie, A two-dimensional method for a family of dispersive shallow water models. SMAI Journal of Computational Mathematics, 6, 187-226, 2020.
  59. I. Gómez, M.J. Castro, C. Parés. High-order well-balanced methods for systems of balance laws: a control-based approach. Applied Mathematics and Computation 394, 125820, 2021.
  60. H. Carrillo, C. Parés, D. Zorío. Lax-Wendroff Approximate Taylor Methods with Fast and Optimized Weighted Essentially Non-oscillatory Reconstructions. Journal of Scientific Computing 86, 15, 2021.
  61. E. Pimentel-García, C. Parés, M. J. Castro, J. Koellermeier, On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems. Applied Mathematics and Computation 388, 125544, 2021.
  62. C. Parés, C. Parés-Pulido. Well-balanced high-order finite difference methods for systems of balance laws. Journal of Computational Physics 425, 109880, 2021. Back to top

Book chapters

  • M.J. Castro, T. Morales de Luna, C. Parés. Well-Balanced Schemes and Path- Conservative Numerical Methods. Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues. Eds: C.-W. Shu, R. Abgrall. Vol. 18:131-175, Elsevier, 2017.
  • C. Parés. Path-conservative numerical schemes for nonconservative hyperbolic systems. Numerical methods for balance laws. Quaderni di Matematica, vol. 24, pp. 67-122. Eds: G. Russo, G. Puppo. Dipartimento di Matematica, Seconda Università di Napoli, 2009. Back to top

Selected referred conference proceedings

  1. N. Aïssiouene, M-O Bristeau, E. Godlewski, A. Mangeney, C. Parés, J. Sainte- Marie. Application of a Combined Finite Element-Finite Volume Method to a 2D Non-hydrostatic Shallow Water Problem. International Conference on Finite Volumes for Complex Applications (Proc. FVCA 2017), pp. 219-226. Springer, 2017.
  2. M.J. Castro, J.T. Frings. On the hyperbolicity of two-and three-layer shallow water equations. Hyperbolic Problems. Theory, Numerics and Applications (Proc. HYP2012), pp. 337-345. AIMS, 2012.
  3. M.J. Castro, E.D. Fernández, J.M. González, A. Mangeney, C. Parés. A high- order finite volume method for nonconservative problems and its application to model submarine avalanches. Integral methods in science and engineering, pp. 91-101. Birkhauser, 2010.
  4. M.L. Muñoz, C. Parés, M.J. Castro. Convergence of path-conservative numerical schemes for hyperbolic systems of balance laws. Numerical mathematics and Advanced Applications (Proc. ENUMATH 2009), pp. 675- 682. Springer, 2010.
  5. M.L. Muñoz, C. Parés. On path-conservative numerical schemes for hyperbolic systems of conservation laws with source terms. Numerical mathematics and advanced applications (Proc. ENUMATH 2007), pp. 305-314. Ed: Springer, 2008.
  6. M.J. Castro, A. Pardo, C. Parés, E. Toro. Well-balanced high-order MUSTA Schemes for non-conservative hyperbolic systems. Numerical mathematics and advanced applications (Proc. ENUMATH 2007), pp. 249-256. Ed: Springer, 2008.
  7. M.J. Castro, E.D. Fern_andez-Nieto, A.M. Ferreiro, J.A. García, C. Parés. High order two dimensional schemes for coupled shallow water-transport systems. Numerical mathematics and advanced applications (Proc. ENUMATH 2007), pp. 241-248. Ed: Springer, 2008.
  8. J.M. Gallardo, M.J. Castro, C. Parés, J.M. González. On a well-balanced high- order finite volume scheme for the shallow water equations with bottom topography and dry areas. Hyperbolic problems: theory, numerics, applications (Proc. HYP2006), pp. 247-258. Ed: Springer, 2008.
  9. C. Parés. Path-conservative numerical schemes for nonconservative hyperbolic systems. Hyperbolic problems: theory, numerics, applications (Proc. HYP2006), pp. 817-824. Ed: Springer, 2008.
  10. M.J. Castro, J.A. López, C. Parés. Analysis of some Finite Volume schemes for the Geostrophic Adjustment problem in a rotating shallow water system. Finite Volumes for Complex Applications V, pp. 273-280. Ed: ISTE, Wiley, 2008.
  11. M.J. Castro, T. Morales, C. Parés. Modeling and simulation of turbidity currents. Finite Volumes for Complex Applications V, pp. 593-600. Ed: ISTE, Wiley, 2008.
  12. M.J. Castro, J.M. Gallardo, M.L. Muñoz, C. Parés. On a general definition of the Godunov method for nonconservative hyperbolic systems. Application to linear balance laws. Numerical mathematics and advanced applications (Proc. ENUMATH 2005), pp. 662-670. Ed: Springer, 2006.
  13. Arregui, J.J. Cendán, C. Vázquez, C. Parés. Optimization of a duality method for the compressible Reynolds equation. Numerical mathematics and advanced applications (Proc. ENUMATH 2005), pp. 319-327. Ed: Springer, 2006.
  14. M.J. Castro, J.A. García, J.M. González, C. Parés. Computational time improvement for some shallow water finite volume models applying parallelization and optimized small matrix computations. Numerical mathematics and advanced applications (Proc. ENUMATH 2005), pp. 288-296. Ed: Springer, 2006.
  15. M.J. Castro, J.A. García, J.M. González, C. Parés. A parallel 2D finite volume scheme for solving the bilayer shallow-water system: modellization of water exchange at the Strait of Gibraltar. Parallel Computational Fluid Dynamics. Multidisciplinary applications, pp. 199-206. Ed: Elsevier, 2005.
  16. M.J. Castro, J.A. García, J.M. González, J. Macías, C. Parés, M.E. Vázquez. Simulation of internal waves in the Strait of Gibraltar using a two-layer Shallow Water model. Mathematical and Numerical Aspects of Wave Propagation. WAVES 2003. Ed: Springer, 2003.
  17. M.J. Castro, J.A. García, J. Macías, C. Parés, M.E. Vázquez. A two-layer numerical model for flows through channels with irregular geometry: application to the water exchange through the Strait of Gibraltar. Finite Volumes for Complex Applications, III, pp. 457-464. Ed: CNRS, 2002.
  18. Valle, C. Parés, J. Macías, M.J. Castro. 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 J.L. Lions, pp. 759-786. Ed: Gauthier-Villars, 1998. Back to top


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