M. Fortin and R. Glowinski, Méthodes de lagrangien augmenté, application à la résolution numérique de problèmes aux limites, 1982.

S. Vincent, A. Sarthou, J. Caltagirone, F. Sonilhac, P. Février et al., Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns, Journal of Computational Physics, vol.230, issue.4, pp.956-983, 2011.
DOI : 10.1016/j.jcp.2010.10.006

A. J. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

C. M. Rhie and W. L. Chow, Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA Journal, vol.21, issue.11, pp.1525-1532, 1983.
DOI : 10.2514/3.8284

F. H. Harlow and J. E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, vol.8, issue.12, pp.2182-2189, 1965.
DOI : 10.1063/1.1761178

J. L. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.6011-6045, 2006.
DOI : 10.1016/j.cma.2005.10.010

J. B. Bell, P. Colella, and H. M. Glaz, A second-order projection method for the incompressible navier-stokes equations, Journal of Computational Physics, vol.85, issue.2, pp.257-2830021, 1989.
DOI : 10.1016/0021-9991(89)90151-4

M. Benzi, Preconditioning Techniques for Large Linear Systems: A Survey, Journal of Computational Physics, vol.182, issue.2, pp.418-4777176, 2002.
DOI : 10.1006/jcph.2002.7176

M. Benzi, G. H. Golub, and J. Liesen, Numerical solution of saddle point problems, Acta Numerica, vol.14, pp.1-137, 2005.
DOI : 10.1017/S0962492904000212

M. Cai, Y. Nokaka, J. B. Bell, B. E. Griffith, and A. Donev, Abstract, Communications in Computational Physics, vol.140, issue.05, pp.1179-1184, 2014.
DOI : 10.1016/j.apnum.2008.01.002

J. L. Guermond and A. Salgado, A splitting method for incompressible flows with variable density based on a pressure Poisson equation, Journal of Computational Physics, vol.228, issue.8, pp.2834-2846, 2009.
DOI : 10.1016/j.jcp.2008.12.036

C. Liu, J. Shen, and X. F. Yang, Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density, Journal of Scientific Computing, vol.515, issue.11, pp.601-622, 2015.
DOI : 10.1007/s10915-014-9867-4

A. Poux, S. Glockner, and M. Azaïez, Improvements on open and traction boundary conditions for Navier???Stokes time-splitting methods, Journal of Computational Physics, vol.230, issue.10, pp.4011-4027, 2011.
DOI : 10.1016/j.jcp.2011.02.024

M. S. Dodd and A. Ferrante, A fast pressure-correction method for incompressible two-fluid flows, Journal of Computational Physics, vol.273, pp.416-434, 2014.
DOI : 10.1016/j.jcp.2014.05.024

J. Caltagirone and S. Vincent, Sur une méthode de pénalisation tensorielle pour la résolution des équations de Navier-Stokes. Comptes Rendus de l'Académie des Sciences Série IIb, pp.607-613, 1999.
DOI : 10.1016/s1620-7742(01)01374-5

P. Angot, J. Caltagirone, and P. Fabrie, A fast vector penalty-projection method for incompressible non-homogeneous or multiphase Navier???Stokes problems, Applied Mathematics Letters, vol.25, issue.11, pp.1681-1688, 2012.
DOI : 10.1016/j.aml.2012.01.037
URL : https://hal.archives-ouvertes.fr/hal-00667121

P. Angot, J. Caltagirone, and P. Fabrie, Fast discrete Helmholtz???Hodge decompositions in bounded domains, Applied Mathematics Letters, vol.26, issue.4, pp.445-451, 2013.
DOI : 10.1016/j.aml.2012.11.006
URL : https://hal.archives-ouvertes.fr/hal-00756959

A. Lemoine, J. Caltagirone, P. Azaiez, and S. Vincent, Discrete Helmholtz???Hodge Decomposition on Polyhedral Meshes Using Compatible Discrete Operators, Journal of Scientific Computing, vol.65, issue.1, pp.10915-10929, 2014.
DOI : 10.1007/s10915-014-9952-8

H. Bhatia, G. Norgard, V. Pascucci, and P. T. Bremer, The Helmholtz-Hodge Decomposition?A Survey, IEEE Transactions on Visualization and Computer Graphics, vol.99, pp.1386-1404, 2012.

J. Caltagirone, Discrete Mechanics, ISTE, 2015.
DOI : 10.1002/9781119058588
URL : https://hal.archives-ouvertes.fr/hal-01079169

J. Caltagirone, Application de la décomposition de Hodge-Helmholtz discrète aux écoulements incompressibles, pp.1-11, 2015.

R. Peyret and T. D. Taylor, Computational Methods for Fluid Flow, 1983.

P. Trontin, S. Vincent, J. Estivalezes, and J. Caltagirone, A subgrid computation of the curvature by a particle/level-set method. Application to a front-tracking/ghost-fluid method for incompressible flows, Journal of Computational Physics, vol.231, issue.20, pp.6990-7010, 2012.
DOI : 10.1016/j.jcp.2012.07.002

S. Vincent, G. Balmigère, J. Caltagirone, and E. Meillot, Eulerian???Lagrangian multiscale methods for solving scalar equations ??? Application to incompressible two-phase flows, Journal of Computational Physics, vol.229, issue.1, pp.73-106, 2010.
DOI : 10.1016/j.jcp.2009.09.007

S. Vincent, J. Caltagirone, P. Lubin, and T. N. Randrianarivelo, An Adaptative Augmented Lagrangian Method for Three-Dimensional Multimaterial Flows. Computers and Fluids, pp.1273-1279, 2004.
DOI : 10.1016/j.compfluid.2004.01.002

S. Vincent and J. Caltagirone, Numerical solving of incompressible Navier-Stokes equations using an original local multigrid refinement method, Comptes Rendus de l'Académie des Sciences SérieIIb, pp.73-80, 2000.
DOI : 10.1016/S1287-4620(00)88419-7

L. F. Richardson and J. A. Gaunt, The Deferred Approach to the Limit. Part I. Single Lattice. Part II. Interpenetrating Lattices, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.226, issue.636-646, pp.299-349, 1927.
DOI : 10.1098/rsta.1927.0008