W. Benz, The Numerical Modelling of Nonlinear Stellar Pulsations, Problems and Prospects, chapter Smooth Particle Hydrodynamics: A Review, NATO ASIS Series, pp.269-287, 1989.

C. Berthon, Contribution à l'analyse numérique des équations de Navier-Stokes compressibles à deux entropies spécifiques. Application à la turbulence compressible, 1998.

M. Coquerelle and G. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, Journal of Computational Physics, vol.227, issue.21, pp.9121-9137, 2008.
DOI : 10.1016/j.jcp.2008.03.041

URL : https://hal.archives-ouvertes.fr/hal-00297673

G. Cottet and P. D. Koumoutsakos, Vortex methods, 2000.
DOI : 10.1017/CBO9780511526442

URL : https://hal.archives-ouvertes.fr/hal-01063292

G. Cottet and A. Magni, TVD remeshing formulas for particle methods, Comptes Rendus Mathematique, vol.347, issue.23-24, pp.1367-1372, 2009.
DOI : 10.1016/j.crma.2009.10.009

URL : https://hal.archives-ouvertes.fr/hal-00321323

G. Cottet, B. Michaux, S. Ossia, and G. Vanderlinden, A Comparison of Spectral and Vortex Methods in Three-Dimensional Incompressible Flows, Journal of Computational Physics, vol.175, issue.2
DOI : 10.1006/jcph.2001.6963

G. Cottet and L. Weynans, Particle methods revisited: a class of high order finite-difference methods, Comptes Rendus Mathematique, vol.343, issue.1, pp.51-56, 2006.
DOI : 10.1016/j.crma.2006.05.001

URL : https://hal.archives-ouvertes.fr/hal-00103200

A. Ghoniem and D. Wee, Modified interpolation kernels for treating diffusion and remeshing in vortex methods, J. Comput. Phys, vol.213, pp.239-263, 2006.

M. W. Evans and F. H. Harlow, The particle-in-cell method for hydrodynamics calculations, 1956.

R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the Royal Astronomical Society, vol.181, issue.3, pp.375-389, 1977.
DOI : 10.1093/mnras/181.3.375

F. H. Harlow, Hydrodynamic Problems Involving Large Fluid Distortions, Journal of the ACM, vol.4, issue.2, p.137, 1957.
DOI : 10.1145/320868.320871

A. Harten, High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics, vol.49, issue.3, pp.357-393, 1983.
DOI : 10.1016/0021-9991(83)90136-5

T. Hou and P. G. Lefloch, Why nonconservative schemes converge to wrong solutions: error analysis, Mathematics of Computation, vol.62, issue.206, pp.497-530, 1994.
DOI : 10.1090/S0025-5718-1994-1201068-0

P. Koumoutsakos and S. Hieber, A lagrangian particle level set method, J. Comp. Phys, vol.210, pp.342-367, 2005.

P. Koumoutsakos and A. Leonard, High-resolution simulations of the flow around an impulsively started cylinder using vortex methods, Journal of Fluid Mechanics, vol.29, issue.-1, pp.1-38, 1995.
DOI : 10.1016/0021-9991(80)90049-2

N. Lanson and J. P. Vila, Renormalized Meshfree Schemes II: Convergence for Scalar Conservation Laws, SIAM Journal on Numerical Analysis, vol.46, issue.4
DOI : 10.1137/S003614290444739X

N. Lanson and J. P. Vila, Convergence des m??thodes particulaires renormalis??es pour les syst??mes de Friedrichs, Comptes Rendus Mathematique, vol.340, issue.6, pp.465-470, 2005.
DOI : 10.1016/j.crma.2004.10.021

R. J. Leveque, Finite-volume methods for hyperbolic problems, 2002.
DOI : 10.1017/CBO9780511791253

A. Magni and G. Cottet, Accurate, non-oscillatory, remeshing schemes for particle methods, to appear in, J. Comput. Phys

A. Magni, Méthodes particulaires avec remaillage : analyse numérique nouveaux schémas et applications pour la simulation d'équations de transport, 2011.

A. Majda and S. Osher, Numerical viscosity and the entropy condition, Communications on Pure and Applied Mathematics, vol.25, issue.6, pp.797-838, 1979.
DOI : 10.1002/cpa.3160320605

J. J. Monaghan, Why Particle Methods Work, SIAM Journal on Scientific and Statistical Computing, vol.3, issue.4, pp.422-433, 1982.
DOI : 10.1137/0903027

J. J. Monaghan, Extrapolating B splines for interpolation, Journal of Computational Physics, vol.60, issue.2, pp.253-262, 1985.
DOI : 10.1016/0021-9991(85)90006-3

J. J. Monaghan, Smoothed Particle Hydrodynamics, Annual Review of Astronomy and Astrophysics, vol.30, issue.1, p.543, 1992.
DOI : 10.1146/annurev.aa.30.090192.002551

B. , B. Moussa, and J. P. Vila, Convergence of sph methods for scalar non linear conservation laws, SIAM J. Numerical. Analysis, vol.37, issue.3

P. Ploumhans, G. S. Winckelmans, J. K. Salmon, A. Leonard, and M. S. Warren, Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows: Application to the Sphere at Re=300, 500, and 1000, Journal of Computational Physics, vol.178, issue.2, pp.427-463, 2002.
DOI : 10.1006/jcph.2002.7035

P. Poncet, Topological aspects of three-dimensional wakes behind rotary oscillating cylinders, Journal of Fluid Mechanics, vol.517, pp.27-53, 2004.
DOI : 10.1017/S0022112004000588

G. A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of Computational Physics, vol.27, issue.1, pp.1-131, 1978.
DOI : 10.1016/0021-9991(78)90023-2

L. Weynans, Méthode particulaire multi-niveaux pour la dynamique des gaz, application au calcul d'écoulements multifluides, 2006.

I. Centre-de-recherche, ?. Grenoble, and . Rhône-alpes, Europe -38334 Montbonnot Saint-Ismier Centre de recherche INRIA Lille ? Nord Europe : Parc Scientifique de la Haute Borne -40, avenue Halley -59650 Villeneuve d'Ascq Centre de recherche INRIA Nancy ? Grand Est : LORIA, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex Centre de recherche INRIA Paris ? Rocquencourt : Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex Centre de recherche INRIA Rennes ? Bretagne Atlantique : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex Centre de recherche INRIA Saclay ? Île-de-France, des Vignes : 4, rue Jacques Monod -91893 Orsay Cedex Centre de recherche INRIA, pp.105-78153, 2004.