Regularization of the Burnett equations for rapid granular flows via relaxation

Physica D: Nonlinear Phenomena

Volumn 150, Issue 3-4, 2001, Pages 207-218

  Jin, Shi ^a   Slemrod, Marshall ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ENTROPY; GRANULAR MATERIALS; HEAT CONVECTION; HEAT FLUX; HEAT LOSSES; RELAXATION PROCESSES; THERMAL EXPANSION; VISCOELASTICITY;

BURNETT EQUATIONS; CHAPMAN-ENSKOG EXPANSION THEORY; RAPID GRANULAR FLOWS;

FLOW OF FLUIDS;

EID: 0035311845     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00224-4     Document Type: Article

References (29)

1. Bobylev A.V. The Chapman-Enskog and Grad methods for solving the Boltzmann equation. Sov. Phys. Dokl. 27:1982;1.
2. Boyle E.J., Massoudi M. A theory of granular materials exhibiting normal stress effects based on Enskog's dense gas theory. Int. J. Eng. Sci. 28:1990;1261-1275.
3. Campbell C.S. Rapid granular flows. Ann. Rev. Fluid Mech. 22:1990;57-92.
4. Chen G.-Q., Levermore C.D., Liu T.-P. Hyperbolic conservation laws with stiff relaxation terms and entropy. Commun. Pure Appl. Math. 47:1994;787-830.
5. Coquel F., Perthame B. Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics. SIAM J. Num. Anal. 35:1998;2223-2249.
6. J.H. Ferziger, H.G. Kaper, Mathematical Theory of Transport Processes in Gases, Elsevier, Amsterdam, 1972.
7. Goldshtein A., Shapiro M. Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech. 282:1995;75-114.
8. Grad H. Asymptotic theory of the Boltzmann equation. Phys. Fluids. 6:1963;147-181.
9. Haff P.K. Grain flow as a fluid mechanical phenomenon. J. Fluid Mech. 134:1986;401-948.
10. Herrmann H.J. Simulation of granular media. Physica A. 191:1992;263-276.
11. Hutter K., Rajagopal K.R. On flows of granular materials. Continuum Mech. Thermodyn. 6:1994;81-139.
12. H.M. Jaeger, S.R. Nagel, R.P. Behringer, The physics of granular materials, Phys. Today (April 1996) 32-38.
13. Jenkins J.T., Richman M.W. Grad's 13-moment system for a dense gas of inelastic particles. Arch. Rat. Mech. Anal. 87:1985;355-377.
14. Jenkins J.T., Richman M.W. Kinetic theory for plane flows of a dense gas of identical, rough inelastic circular disks. Phys. Fluids. 28:1985;3485-3494.
15. Jenkins J.T., Richman M.W. Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in the dilute dense gas limit. J. Fluid Mech. 192:1988;313-328.
16. S. Jin, M. Slemrod, Regularization of the Burnett equations via relaxation, J. Stat. Phys. 103 (2001), to appear.
17. Jin S., Xin Z.P. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Commun. Pure Appl. Math. 48:1995;235-276.
18. D.D. Joseph, Fluid Dynamics of Viscoelastic Liquids, Springer, Berlin, 1990.
19. Levermore C.D. Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83:1996;1021-1065.
20. Levermore C.D., Morokoff W.J. The Gaussian moment closure for gas dynamics. SIAM J. Appl. Math. 59:1998;72-96.
21. A.V. Luk'shin, Hydrodynamical limit for the Boltzmann equation and its different analogs, in: Numerical and Analytical Methods in Rarefied Gas Dynamics, Moscow Aviation Institute, Moscow, 1986, pp. 37-43.
22. A.V. Luk'shin, The Cauchy problem for the Boltzmann equation: hydrodynamical limit, in: Numerical Methods in Mathematical Physics, Moscow State University, Moscow, 1986, pp. 61-91.
23. Lun C.K.K., Savage S.B., Jeffrey D.J., Chepurniy N. Kinetic theories of granular flow: inelastic particles in a Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140:1984;223-256.
24. Lun C.K.K. Kinetic theory of granular flow of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 223:1991;539-559.
25. I. Müller, T. Ruggeri, Rational Extended Thermodynamics, 2nd Edition, Springer, Berlin, 1998.
26. Sela N., Goldhirsch I. Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Flud Mech. 361:1998;41-74.
27. Slemrod M. Constitutive relations for monotomic gases based on a generalized rational approximation to the sum of the Chapman-Enskog expansion. Arch. Rat. Mech. Anal. 150:1999;1-22.
28. M. Slemrod, Constitutive relations for rapid granular flow of smooth spheres: generalized rational approximation to the sum of the Chapman-Enskog expansion, J. Diff. Eq. 169 (2001) 549-566.
29. C. Truesdell, R.G. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Academic Press, New York, 1980.