Free Access
Issue
ESAIM: M2AN
Volume 47, Number 1, January-February 2013
Page(s) 57 - 81
DOI https://doi.org/10.1051/m2an/2012019
Published online 31 July 2012
  1. B. Ben Moussa and J.P. Vila, Convergence of SPH methods for scalar nonlinear conservation laws. SIAM J. Numer. Anal. 37 (2000) 863–887. [CrossRef] [MathSciNet] [Google Scholar]
  2. W. Benz, The Numerical Modelling of Nonlinear Stellar Pulsations, Problems and Prospects, a review, in Smooth Particle Hydrodynamics : NATO ASIS Series (1989) 269–287. [Google Scholar]
  3. C. Berthon, Contribution à l’analyse numérique des équations de Navier-Stokes compressibles à deux entropies spécifiques. Application à la turbulence compressible. Ph.D. thesis, Université Paris VI (1998). [Google Scholar]
  4. M. Coquerelle and G.-H. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies. J. Comput. Phys. 227 (2008) 9121–9137. [CrossRef] [Google Scholar]
  5. G.-H. Cottet and P.D. Koumoutsakos, Vortex methods. Cambridge University Press (2000). [Google Scholar]
  6. G.-H. Cottet and A. Magni, TVD remeshing schemes for particle methods. C. R. Acad. Sci. Paris, Ser. I 347 (2009) 1367–1372. [CrossRef] [Google Scholar]
  7. G.-H. Cottet and L. Weynans, Particle methods revisited : a class of high-order finite-difference schemes. C. R. Acad. Sci. Paris, Ser. I 343 (2006) 51–56. [Google Scholar]
  8. G.-H. Cottet, B. Michaux, S. Ossia and G. Vanderlinden, A comparison of spectral and vortex methods in three-dimensional incompressible flow. J. Comput. Phys. 175 (2002) 702–712. [CrossRef] [Google Scholar]
  9. M.W. Evans and F.H. Harlow, The particle-in-cell method for hydrodynamics calculations. Technical Report, Los Alamos Scientific Laboratory (1956). [Google Scholar]
  10. A. Ghoniem and D. Wee, Modified interpolation kernels for treating diffusion and remeshing in vortex methods. J. Comput. Phys. 213 (2006) 239–263. [CrossRef] [Google Scholar]
  11. R.A. Gingold and J.J. Monaghan, Smoothed particle hydrodynamics : theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181 (1977) 375–389. [Google Scholar]
  12. F.H. Harlow, Hydrodynamic problems involving large fluid distorsion. J. Assoc. Comput. Mach. 4 (1957) 137–142. [CrossRef] [Google Scholar]
  13. A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357–393. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  14. T. Hou and P.G. Lefloch, Why non-conservative schemes converge to wrong solutions : error analysis. Math. Comput. 62 (1994) 497–530. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  15. P. Koumoutsakos and S. Hieber. A Lagrangian particle level set method. J. Comput. Phys. 210 (2005) 342–367. [CrossRef] [Google Scholar]
  16. P. Koumoutsakos and A. Leonard, High resolution simulations of the flow around an impulsively started cylinder using vortex methods. J. Fluid Mech. 296 (1995) 1–38. [CrossRef] [Google Scholar]
  17. N. Lanson and J.P. Vila, Convergence des méthodes particulaires renormalisées pour les systèmes de Friedrichs. C. R. Acad. Sci. Paris, Ser. I 349 (2005) 465–470. [CrossRef] [Google Scholar]
  18. N. Lanson and J.P. Vila, Renormalized meshfree schemes II : convergence for scalar conservation laws. SIAM J. Numer. Anal. 46 (2008) 1935–1964. [CrossRef] [MathSciNet] [Google Scholar]
  19. R.J. LeVeque, Finite-volume methods for hyperbolic problems. Cambridge University Press (2002). [Google Scholar]
  20. A. Magni, Méthodes particulaires avec remaillage : analyse numérique nouveaux schémas et applications pour la simulation d’équations de transport. Ph.D. thesis, Université de Grenoble. Available on : http://tel.archives-ouvertes.fr/ tel-00623128/fr/ (2011). [Google Scholar]
  21. A. Magni and G.-H. Cottet, Accurate, non-oscillatory, remeshing schemes for particle methods. J. Comput. Phys. 231 (2012) 152–172. [CrossRef] [Google Scholar]
  22. A. Majda and S. Osher, Numerical viscosity and the entropy condition. Commun. Pure Appl. Math. 32 (1979) 797–838. [CrossRef] [Google Scholar]
  23. J.J. Monaghan, Why particle methods work. SIAM J. Sci. Stat. Comput 3 (1982) 422–433. [CrossRef] [Google Scholar]
  24. J.J. Monaghan, Extrapolating B-splines for interpolation. J. Comput. Phys. 60 (1985) 253–262. [CrossRef] [Google Scholar]
  25. J.J. Monaghan, Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30 (1992) 543–574. [CrossRef] [Google Scholar]
  26. 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. J. Comput. Phys. 178 (2002) 427–463. [CrossRef] [Google Scholar]
  27. P. Poncet, Topological aspects of the three-dimensional wake behind rotary oscillating circular cylinder. J. Fluid Mech. 517 (2004) 27–53. [CrossRef] [Google Scholar]
  28. G.A. Sod, A survey of several finite-difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27 (1978) 1–131. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  29. L. Weynans, Méthode particulaire multi-niveaux pour la dynamique des gaz, application au calcul d’écoulements multifluides. Ph.D. thesis, Université Joseph Fourier. Available on : http://tel.archives-ouvertes.fr/tel-00121346/en/ (2006). [Google Scholar]

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