Bibliography

Major publications by the team in recent years

• 1E. Audusse, M.-O. Bristeau, M. Pelanti, J. Sainte-Marie.
  
  Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation, in: J. Comput. Phys., 2011, vol. 230, pp. 3453-3478.
  
  http://dx.doi.org/10.1016/j.jcp.2011.01.042
• 2E. Audusse, M.-O. Bristeau, B. Perthame, J. Sainte-Marie.
  
  A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation, in: ESAIM Math. Model. Numer. Anal., 2011, vol. 45, pp. 169-200.
  
  http://dx.doi.org/10.1051/m2an/2010036
• 3M.-O. Bristeau, B. Di Martino, C. Guichard, J. Sainte-Marie.
  
  Layer-averaged Euler and Navier-Stokes equations, Sep 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01202042
• 4J. Sainte-Marie.
  
  Vertically averaged models for the free surface Euler system. Derivation and kinetic interpretation, in: Math. Models Methods Appl. Sci. (M3AS), 2011, vol. 21, n^o 3, pp. 459-490.
  
  http://dx.doi.org/10.1142/S0218202511005118

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 5N. Aissiouene.
  
  Numerical analysis and discrete approximation of a dispersive shallow water model, Pierre et Marie Curie, Paris VI, December 2016.
  
  https://hal.archives-ouvertes.fr/tel-01418676

Articles in International Peer-Reviewed Journals

• 6N. Aissiouene, M.-O. Bristeau, E. Godlewski, J. Sainte-Marie.
  
  A combined finite volume - finite element scheme for a dispersive shallow water system, in: Networks and Heterogeneous Media (NHM), January 2016, vol. 11, n^o 1, pp. 1-27.
  
  https://hal.inria.fr/hal-01160718
• 7E. Audusse, F. Bouchut, M.-O. Bristeau, J. Sainte-Marie.
  
  Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system, in: Mathematics of Computation, November 2016, vol. 85, pp. 2815-2837. [ DOI : 10.1090/mcom/3099 ]
  
  https://hal.inria.fr/hal-01063577
• 8J.-F. Babadjian, C. Mifsud, N. Seguin.
  
  Relaxation approximation of Friedrich's systems under convex constraints, in: Networks and Heterogeneous Media, 2016, vol. 11, n^o 2, pp. 223 - 237. [ DOI : 10.3934/nhm.2016.11.223 ]
  
  https://hal.archives-ouvertes.fr/hal-01157484
• 9F. Bouchut, I. R. Ionescu, A. Mangeney.
  
  An analytic approach for the evolution of the static/flowing interface in viscoplastic granular flows, in: Communications in Mathematical Sciences, 2016, vol. 14, n^o 8, pp. 2101-2126. [ DOI : 10.4310/CMS.2016.v14.n8.a2 ]
  
  https://hal-upec-upem.archives-ouvertes.fr/hal-01081213
• 10C. Cancès, F. Coquel, E. Godlewski, H. Mathis, N. Seguin.
  
  Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations, in: Communications in Mathematical Sciences, 2016, vol. 14, n^o 1, pp. 1-30.
  
  https://hal.archives-ouvertes.fr/hal-00852101
• 11D. Kazerani.
  
  Global existence for small data of the viscous Green-Naghdi type equations, in: Journal of Differential Equations, July 2016, vol. 261, n^o 1, pp. 762-796. [ DOI : 10.1016/j.jde.2016.03.022 ]
  
  https://hal.archives-ouvertes.fr/hal-01111941
• 12D. Kazerani.
  
  The symmetric structure of the Green-Naghdi type equations, in: Communications in Mathematical Sciences, August 2016, vol. 14, n^o 7, pp. 1925-1946. [ DOI : 10.4310/CMS.2016.v14.n7.a7 ]
  
  https://hal.archives-ouvertes.fr/hal-01074488
• 13M. Lachowicz, H. Leszczyński, M. Parisot.
  
  A simple kinetic equation of swarm formation: blow–up and global existence, in: Applied Mathematics Letters, January 2016. [ DOI : 10.1016/j.aml.2016.01.008 ]
  
  https://hal.inria.fr/hal-01241998
• 14M. Lachowicz, M. Parisot, Z. Szymańska.
  
  Intracellular protein dynamics as a mathematical problem, in: Discrete and Continuous Dynamical Systems - Series B (DCDS-B), February 2016.
  
  https://hal.inria.fr/hal-01152399
• 15C. Mifsud, B. Després, N. Seguin.
  
  Dissipative formulation of initial boundary value problems for Friedrichs' systems, in: Communications in Partial Differential Equations, January 2016, vol. 41, n^o 1. [ DOI : 10.1080/03605302.2015.1103750 ]
  
  https://hal.archives-ouvertes.fr/hal-01074542
• 16M. Parisot, M. Lachowicz.
  
  A Kinetic Model for the formation of Swarms with nonlinear interactions, in: Kinetic and Related Models , March 2016, vol. 9, n^o 1, 33 p. [ DOI : 10.3934/krm.2016.9.131 ]
  
  https://hal.inria.fr/hal-01152397
• 17M. Parisot, J.-P. Vila.
  
  Centered-potential regularization for the advection upstream splitting method, in: SIAM Journal on Numerical Analysis, 2016.
  
  https://hal.inria.fr/hal-01152395

Other Publications

• 18N. Aissiouene, T. Amtout, M. Brachet, E. Frénod, R. Hild, C. Prud 'homme, A. Rousseau, S. Salmon.
  
  Hydromorpho: A coupled model for unsteady Stokes/Exner equations and numerical results with Feel++ library, February 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01266223
• 19E. Audusse, C. Chalons, P. Ung.
  
  A simple three-wave Approximate Riemann Solver for the Saint-Venant–Exner equations, August 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01204754
• 20M.-O. Bristeau, D. Froger, R. Hamouda, A. Mangeney, J. Sainte-Marie, M. Vallée.
  
  Numerical simulations of 3d hydrostatic Navier-Stokes system with free surface, November 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01393147
• 21C. Cancès, C. Guichard.
  
  Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure, 2016, to appear in Foundations of Computational Mathematics.
  
  https://hal.archives-ouvertes.fr/hal-01119735
• 22B. Di Martino, B. Haspot, Y. Penel.
  
  Global stability of weak solutions for a multilayer Saint-Venant model with interactions between the layers, December 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01407886
• 23J. Droniou, R. Eymard, T. Gallouët, C. Guichard, R. Herbin.
  
  The gradient discretisation method : A framework for the discretisation and numerical analysis of linear and nonlinear elliptic and parabolic problems, November 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01382358
• 24R. Eymard, P. Feron, C. Guichard.
  
  Family of convergent numerical schemes for the incompressible Navier-Stokes equations, October 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01382924
• 25E. D. Fernandez-Nieto, M. Parisot, Y. Penel, J. Sainte-Marie.
  
  Layer-averaged approximations for inviscid flow models, June 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01324012
• 26E. Godlewski, M. Parisot, J. Sainte-Marie, F. Wahl.
  
  Congested shallow water type model : roof modelling in free surface flow, September 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01368075
• 27M. Lachowicz, H. Leszczyński, M. Parisot.
  
  Blow-up and global existence for a kinetic equation of swarm formation, 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01370006
• 28C. Lusso, F. Bouchut, A. Ern, A. Mangeney.
  
  A free interface model for static/flowing dynamics in thin-layer flows of granular materials with yield: simple shear simulations and comparison to experiments, December 2016, working paper or preprint.
  
  https://hal-upec-upem.archives-ouvertes.fr/hal-00992309
• 29C. Lusso, F. Bouchut, A. Ern, A. Mangeney.
  
  Explicit solutions to a free interface model for the static/flowing transition in thin granular flows, August 2016, working paper or preprint.
  
  https://hal-upec-upem.archives-ouvertes.fr/hal-01180686
• 30C. Lusso, A. Ern, F. Bouchut, A. Mangeney, M. Farin, O. Roche.
  
  Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse, December 2016, working paper or preprint. [ DOI : 10.1016/j.jcp.2016.12.036 ]
  
  https://hal-upec-upem.archives-ouvertes.fr/hal-01133786

References in notes

• 31E. Audusse.
  
  A multilayer Saint-Venant model : Derivation and numerical validation, in: Discrete Contin. Dyn. Syst. Ser. B, 2005, vol. 5, n^o 2, pp. 189-214.
• 32F. Bouchut, J. Sommer, V. Zeitlin.
  
  Frontal geostrophic adjustment and nonlinear wave phenomena in one-dimensional rotating shallow water. part 2. high-resolution numerical simulations, in: J. Fluid Mech., 2004, vol. 514, pp. 35–63.
• 33F. Bouchut, V. Zeitlin.
  
  A robust well-balanced scheme for multi-layer shallow water equations, in: Discrete Contin. Dyn. Syst. Ser. B, 2010, vol. 13, pp. 739-758.
• 34M. Castro, J. García-Rodríguez, J. González-Vida, J. Macías, C. Parés, M. Vázquez-Cendón.
  
  Numerical simulation of two-layer shallow water flows through channels with irregular geometry, in: J. Comput. Phys., 2004, vol. 195, n^o 1, pp. 202–235.
• 35S. Dellacherie.
  
  Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number, in: J. Comput. Phys., 2010, vol. 229, n^o 4, pp. 978–1016.
• 36B. Després, C. Buet.
  
  The structure of well-balanced schemes for Friedrichs systems with linear relaxation, in: Appl. Math. Comput., 2016, vol. 272, pp. 440–459.
• 37N. Goutal, M. Parisot, F. Zaoui.
  
  A 2D reconstruction for the transverse coupling of shallow water models, in: Int. J. Numer. Methods Fluids, 2014, vol. 75, n^o 11, pp. 775–799.