Free access
Issue
ESAIM: M2AN
Volume 39, Number 5, September-October 2005
Page(s) 931 - 963
DOI http://dx.doi.org/10.1051/m2an:2005041
Published online 15 September 2005
  1. M.R. Archambault, C.F. Edwards and R.W. MacCormack, Computation of spray dynamics by moment transport equations I: Theory and development. Atomization Spray 13 (2003) 63–87. [CrossRef]
  2. M.R. Archambault, C.F. Edwards and R.W. MacCormack, Computation of spray dynamics by moment transport equations II: Application to calculation of a quasi-one-dimensional spray. Atomization Spray 13 (2003) 89–115. [CrossRef]
  3. J.C. Beck and A.P. Watkins, On the development of spray submodels based on droplet size moments. J. Comput. Phys. 182 (2002) 1–36. [CrossRef]
  4. J.C. Beck and A.P. Watkins, The droplet number moments approach to spray modeling: The development of heat and mass transfer sub-models. Int. J. Heat Fluid Flow 24 (2003) 242–259. [CrossRef]
  5. A.V. Bobylev and T. Ohwada, The error of the splitting scheme for solving evolutionary equations. Appl. Math. Lett. 14 (2001) 45–48. [CrossRef] [MathSciNet]
  6. F. Bouchut, On zero pressure gas dynamics. Advances in Kinetic Theory and Computing, Selected Papers, Ser. Adv. Math. Appl. Sci. 22 (1994) 171–190.
  7. F. Bouchut, S. Jin and X. Li, Numerical approximations of pressureless and isothermal gas dynamics. SIAM J. Numer. Anal. 41-1 (2003) 135–158. [CrossRef]
  8. R. Clift, J.R. Grace and M.E. Weber, Bubbles, drops and particles. Academic Press (1978).
  9. C.T. Crowe, Review - Numerical methods for dilute gas-particle flows. Trans. ASME J. Fluids Eng. 104 (1982) 297–303. [CrossRef]
  10. C. Dafermos, Generalized characteristics in hyperbolic systems of conservation laws. Arch. Rational Mech. Anal. 107 (1989) 127–155. [CrossRef] [MathSciNet]
  11. K. Domelevo, Analyse mathématique et numérique d'une modélisation cinétique d'un brouillard de gouttelettes dans un écoulement gazeux turbulent. Ph.D. Thesis, École Polytechnique, France (1996).
  12. K. Domelevo, The kinetic sectional approach for noncolliding evaporating sprays. Atomization Spray 11 (2001) 291–303.
  13. D.A. Drew, Mathematical modeling of two-phase flows. Annu. Rev. Fluid. Mech. 15 (1983) 261–291. [CrossRef]
  14. G. Dufour, Un modèle multi-fluide Eulerien pour les écoulements diphasiques à inclusions dispersées. Ph.D. Thesis, Université Toulouse III, France (2005).
  15. J.K. Dukowicz, A particle-fluid numerical model for liquid sprays. J. Comput. Phys. 35 (1980) 229–253. [CrossRef] [MathSciNet]
  16. J. Dupays, Contribution à l'étude du rôle de la phase condensée dans la stabilité d'un propulseur à propergol solide pour lanceur spatial. Ph.D. Thesis, Institut National Polytechnique de Toulouse, France (1996).
  17. H. Grad, On the kinetic theory of rarefied gases. Comm. Pure Appl. Math. 2 (1949) 331–407. [CrossRef] [MathSciNet]
  18. J.B. Greenberg, I. Silverman and Y. Tambour, On the origin of spray sectional conservation equations. Combustion Flame 93 (1993) 90–96. [CrossRef]
  19. A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes III. J. Comput. Phys. 126 (1987) 231–303. [CrossRef] [MathSciNet]
  20. J.J. Hylkema, Modélisation cinétique et simulation numérique d'un brouillard dense de gouttelettes. Applications aux propulseurs à poudre. Ph.D. Thesis, ENSAE, France (1999).
  21. M. Ishii, Thermo-fluid dynamics of two-phase flows. Eyrolles, Paris (1975).
  22. F. Laurent, Analyse numérique d'une méthode multi-fluide Eulérienne pour la description de sprays qui s'évaporent. C. R. Acad. Sci. Paris Ser. I 334 (2002) 417–422.
  23. F. Laurent, Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays. To be submitted.
  24. F. Laurent and M. Massot, Multi-fluid modeling of laminar poly-disperse spray flames: origin, assumptions and comparison of sectional and sampling methods. Combust. Theor. Model. 5 (2001) 537–572. [CrossRef]
  25. F. Laurent, M. Massot and P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays. J. Comput. Phys. 194 (2004) 505–543. [CrossRef] [MathSciNet]
  26. F. Laurent, V. Santoro, M. Noskov, M.D. Smooke, A. Gomez and M. Massot, Accurate treatment of size distribution effects in polydisperse spray diffusion flames: multi-fluid modelling, computations and experiments. Combust. Theor. Model. 8 (2004) 385–412. [CrossRef]
  27. C.D. Levermore, Moment closure hierarchies for kinetics theories. J. Statist. Phys. 83 (1996) 1021–1065. [CrossRef] [MathSciNet]
  28. D. Levy, G. Puppo and G. Russo, On the behavior of the total variation in CWENO methods for conservation laws. Appl. Numer. Math. 33 (2000) 407–414. [CrossRef] [MathSciNet]
  29. R. Maxey and J. Riley, Equation of motion of a small rigid sphere in a non-unifom flow. Phys. Fluids 26 (1983) 883–889. [NASA ADS] [CrossRef]
  30. P.J. O'Rourke, Collective drop effects on vaporizing liquid sprays. Ph.D. Thesis, Los Alamos national Laboratory, New Mexico 87545 (1981).
  31. F. Poupaud and M. Rascle, Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients. Comm. P.D.E 22 (1997) 337–358.
  32. D. Ramkrishna and A.G. Fredrickson, Population balances: Theory and applications to particulate systems in engineering. Academic Press (2000).
  33. M. Rüger, S. Hohmann, M. Sommerfeld and G. Kohnen, Euler-Lagrange calculations of turbulent sprays: the effect of droplet collisions and coalescence. Atomization Spray 10 (2000).
  34. O. Simonin, Modélisation numérique des écoulements turbulents diphasiques à inclusions dispersées. École de Printemps de Mécanique des Fluides numériques, Aussois (1991).
  35. O. Simonin, Continuum modeling of dispersed two-phase flows. Combustion and turbulence in two-phase flows. Lecture Series 1996-02, Von Karman Inst. for fluid dyn. (1996).
  36. G. Strang, On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 507–517.
  37. Y. Tambour, A Lagrangian sectional approach for simulating droplet size distribution of vaporizing fuel sprays in a turbulent jet. Combustion Flame 60 (1985) 15–28. [CrossRef]
  38. B. Van Leer, A second-order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 101–136. [NASA ADS] [CrossRef]
  39. F.A. Williams, Spray combustion and atomization. Phys. Fluids 1 (1958) 541–555. [CrossRef]
  40. F.A. Williams, Combustion Theory. Addison-Wesley Publishing (1985).
  41. D.L. Wright, R. McGraw and D.E. Rosner, Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations. J. Colloid Interf. Sci. 236 (2001) 242–251. [CrossRef]

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