Math. Model. Nat. Phenom.
Volume 6, Number 4, 2011Granular hydrodynamics
|Page(s)||151 - 174|
|Published online||18 July 2011|
- A. E. Beylich. Solving the kinetic equation for all Knudsen numbers. Phys. Fluids 12 (2000), 444–465. [CrossRef]
- G. A. Bird. Molecular gas dynamics and the direct simulation theory of gas flows. Oxford University Press, 1994.
- M. Bisi, G. Spiga, and G. Toscani. Grad’s equations and hydrodynamics for weakly inelastic flows. Phys. Fluids 16 (2004), 4235–4247. [CrossRef] [MathSciNet]
- A. V. Bobylev. The Chapman-Enskog and Grad methods for solving the Boltzmann equation. Sov. Phys., dokl 27 (1982), 29–31.
- 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]
- J. J. Brey, W.-J Ruiz-Montero, and F. Moreno.. Hydrodynamics of an open vibrated system. Phys. Rev. E 63 (2001), 061305. [CrossRef]
- N.V. Briliantov and T. Pöschel. Kinetic theory of granular gases. Oxford University Press, Oxford, 2004.
- C. S. Campbell. Rapid granular flows. Annu. Rev. Fluid Mech. 22 (1990), 57–92. [CrossRef]
- C. Cercignani. Theory and application of the Boltzmann equation. Scottish Acad. Press, Edinburgh and London, 1975.
- S. Chapman and T. G. Cowling. The mathematical theory of nonuniform gases. Cambridge University Press, Cambridge, 1970.
- 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]
- V. Garzó and J. W. Dufty. Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59 (1998), 5895–5911.
- I. Goldhirsch. Rapid granular flows. Annu. Rev. Fluid Mech. 35 (2003), 267–293. [CrossRef]
- 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).
- 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]
- H. Grad. On the kinetic theory of rarefied gases. Commun. Pure Appl. Maths 2 (1949), 331–407. [CrossRef] [MathSciNet]
- 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]
- 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.
- M. N. Kogan. Rarefied gas dynamics. Plenum, New York, 1969.
- C. D. Levermore and W.J. Morokoff. The gaussian moment closure for gas dynamics. SIAM J.App. Math. 59 (1998), 72–96. [CrossRef]
- D. Mintzer. Generalized orthogonal polynomial solutions of the Boltzmann equation. Phys. Fluids 8 (1965), 1076–1090. [CrossRef]
- 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]
- 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]
- Y. G. Ohr. Improvement of the grad 13 moment method for strong shock waves. Phys. Fluids 13 (2001), 2105–2114. [CrossRef] [MathSciNet]
- R. Ramirez, D. Risso, R. Soto, and P. Cordero. Hydrodynamic theory for granular gases. Phys. Rev. E 62 (2000), 2521–2530. [CrossRef]
- P. Rosenau, Extending hydrodynamics via the regularization of the Chapman-Enskog expansion. Phys. Rev. A 40 (1989), 7193–7196. [CrossRef] [MathSciNet] [PubMed]
- 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]
- R. Soto. Granular systems on a vibrating wall: the kinetic boundary condition. Phys. Rev. E 69 (2004), 61305–61310. [CrossRef]
- H. Struchtrup and M. Torrilhon. Regularization of Grad’s 13 momemt equations: derivation and linear analysis. Phys. Fluids 15 (2003), 2668–2680. [CrossRef] [MathSciNet]
- 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]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.