Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 4, 2011
Granular hydrodynamics
Page(s) 151 - 174
DOI https://doi.org/10.1051/mmnp/20116407
Published online 18 July 2011
  1. A. E. Beylich. Solving the kinetic equation for all Knudsen numbers. Phys. Fluids 12 (2000), 444–465. [CrossRef] [Google Scholar]
  2. G. A. Bird. Molecular gas dynamics and the direct simulation theory of gas flows. Oxford University Press, 1994. [Google Scholar]
  3. M. Bisi, G. Spiga, and G. Toscani. Grad’s equations and hydrodynamics for weakly inelastic flows. Phys. Fluids 16 (2004), 4235–4247. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. V. Bobylev. The Chapman-Enskog and Grad methods for solving the Boltzmann equation. Sov. Phys., dokl 27 (1982), 29–31. [Google Scholar]
  5. J. J. Brey, J.W. Dufty, C. S. Kim and A. Santos. Hydrodynamics for granular flows at low density. Phys. Rev. E 58 (1997), 4638–4653. [CrossRef] [Google Scholar]
  6. J. J. Brey, W.-J Ruiz-Montero, and F. Moreno.. Hydrodynamics of an open vibrated system. Phys. Rev. E 63 (2001), 061305. [CrossRef] [Google Scholar]
  7. N.V. Briliantov and T. Pöschel. Kinetic theory of granular gases. Oxford University Press, Oxford, 2004. [Google Scholar]
  8. C. S. Campbell. Rapid granular flows. Annu. Rev. Fluid Mech. 22 (1990), 57–92. [CrossRef] [Google Scholar]
  9. C. Cercignani. Theory and application of the Boltzmann equation. Scottish Acad. Press, Edinburgh and London, 1975. [Google Scholar]
  10. S. Chapman and T. G. Cowling. The mathematical theory of nonuniform gases. Cambridge University Press, Cambridge, 1970. [Google Scholar]
  11. L. García-Colin, R. M. Velasco, and F. J. Uribe. Inconsistency in the moment’s method for solving the Boltzmann equation. J. Non-Equilib. Thermodyn. 29 (2004), 257–277. [CrossRef] [Google Scholar]
  12. V. Garzó and J. W. Dufty. Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59 (1998), 5895–5911. [Google Scholar]
  13. I. Goldhirsch. Rapid granular flows. Annu. Rev. Fluid Mech. 35 (2003), 267–293. [CrossRef] [Google Scholar]
  14. S. H. Noskowicz, D. Serero, and O. Bar-Lev. Generating functions and kinetic theory: a computer aided method. Application: constitutive relations for granular gases up to moderate densities. in preparation (2011). [Google Scholar]
  15. A. Goldshtein and M. Shapiro. Mechanics of collisional motion of granular materials, part 1: general hydrodynamic equations. J. Fluid Mech. 282 (1995), 75–114. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  16. H. Grad. On the kinetic theory of rarefied gases. Commun. Pure Appl. Maths 2 (1949), 331–407. [CrossRef] [MathSciNet] [Google Scholar]
  17. I. N. Ivchenko, S. K. Loyalka, and R.V. Thompson. The polynomial expansion method for boundary value problems of transport in rarefied gases. Z. angew. Math. Phys. 49 (1998), 955–966. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. T. Jenkins and M. W. Richman. Grad’s 13-moment system for a dense gas of inelastic spheres. Arch. Rational. Mech. Anal. 28 (2001), 355–377. [Google Scholar]
  19. M. N. Kogan. Rarefied gas dynamics. Plenum, New York, 1969. [Google Scholar]
  20. C. D. Levermore and W.J. Morokoff. The gaussian moment closure for gas dynamics. SIAM J.App. Math. 59 (1998), 72–96. [CrossRef] [Google Scholar]
  21. D. Mintzer. Generalized orthogonal polynomial solutions of the Boltzmann equation. Phys. Fluids 8 (1965), 1076–1090. [CrossRef] [Google Scholar]
  22. R. Nagai, H. Honma, K. Maeno, and A. Sakurai. Shock wave solution of the Boltzmann kinetic equation in a 13-moment approximation. Shock Waves 13 (2003), 213–220. [CrossRef] [Google Scholar]
  23. S. H. Noskowicz, O. Bar-Lev, D. Serero, and I. Goldhirsch. Computer-aided kinetic theory and granular gases. Europhys. Lett. 79 (2007), 60001. [CrossRef] [MathSciNet] [Google Scholar]
  24. Y. G. Ohr. Improvement of the grad 13 moment method for strong shock waves. Phys. Fluids 13 (2001), 2105–2114. [CrossRef] [MathSciNet] [Google Scholar]
  25. R. Ramirez, D. Risso, R. Soto, and P. Cordero. Hydrodynamic theory for granular gases. Phys. Rev. E 62 (2000), 2521–2530. [CrossRef] [Google Scholar]
  26. P. Rosenau, Extending hydrodynamics via the regularization of the Chapman-Enskog expansion. Phys. Rev. A 40 (1989), 7193–7196. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. N. Sela and I. Goldhirsch. Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361 (1998), 41–74. [CrossRef] [MathSciNet] [Google Scholar]
  28. R. Soto. Granular systems on a vibrating wall: the kinetic boundary condition. Phys. Rev. E 69 (2004), 61305–61310. [CrossRef] [Google Scholar]
  29. H. Struchtrup and M. Torrilhon. Regularization of Grad’s 13 momemt equations: derivation and linear analysis. Phys. Fluids 15 (2003), 2668–2680. [CrossRef] [MathSciNet] [Google Scholar]
  30. T. Thatcher, Y. Zheng, and H. Struchtrup. Boundary conditions for Grad’s 13 moment equations. Progress in Computational Fuid Dynamics 8 (2008), 69–83. [CrossRef] [Google Scholar]

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