Models of low-speed flow for near-critical fluids with gravitational and capillary effects

Quarterly of Applied Mathematics

Volumn 58, Issue 1, 2000, Pages 103-125

  Denny, D L ^a   Pego, R L ^b  

^a JAMES MADISON UNIVERSITY   (United States)

^b Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CAPILLARY FLOW; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL GEOMETRY; GRAVITATIONAL EFFECTS; INITIAL VALUE PROBLEMS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS;

MACH NUMBER; SINGLE-PHASE FLUIDS;

COMPRESSIBLE FLOW;

EID: 0033896314     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1738560     Document Type: Article

References (36)

1. D. M. Anderson, G. B. McFadden, and A. A. Wheeler, Diffuse-interface methods in fluid mechanics, Ann. Rev. Fluid Mech. 30, 139-165 (1998)
2. G. K. Batchelor, The conditions for dynamical similarity of motions of a frictionless perfect-gas atmosphere, Quart. J. Roy. Meteo. Soc. 79, 224-235 (1953)
3. R. F. Berg, Thermal equilibration near the critical point: Effects due to three dimensions and gravity, Phys. Rev. E 48, 1799-1805 (1993)
4. H. Boukari, M. E. Briggs, J. N. Shaumeyer, and R. W. Gammon, Critical speeding up observed, Phys. Rev. Lett. 65, 2654-2657 (1990)
5. H. Boukari, R. Pego, and R. W. Gammon, Calculation of the dynamics of gravity-induced density profiles near a liquid-vapor critical point, Phys. Rev. E 52, 1614-1625 (1995)
6. H. Boukari, J. N. Shaumeyer, M. E. Briggs, and R. W. Gammon, Critical speeding up in pure fluids, Phys. Rev. A 41, 2260-2263 (1990)
7. A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, 3rd. ed., Springer-Verlag, New York, 1993
8. D. L. Denny and R. L. Pego, Solutions for a model of low-speed flow for highly compressible fluids with capillary effects, in preparation
9. J. E. Dunn and J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal. 88, 95-133 (1985)
10. D. Durran, Improving the anelastic approximation, J. Atmos. Sci. 46, 1453-1461 (1989)
11. J. A. Dutton and G. H. Fichtl, Approximate equations of motion for gases and liquids, J. Atmos. Sci. 26, 241-254 (1969)
12. P. Embid, Well-posedness of the Nonlinear Equations for Zero Mach Number Combustion, Ph. D. Thesis, University of California, Berkeley, 1984
13. R. Gammon, personal communication. Also see the ZENO home page at the URL http://roissy.umd.edu/. The experimental design is described at the URL http://roissy. umd.edu/usmp3/reminder.html.
14. 6 under reduced gravity, J. Coll. Internat. Sci. 178, 368-370 (1996)
15. C. Ikier, H. Klein, and D. Woermann, Density equilibration in a near-critical fluid under reduced gravity, Ber. Bunsenges. Phys. Chem. 100 (8), 1308-1311 (1996)
16. S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math. 34, 481-524 (1981)
17. A. B. Kogan, F. Zhong, and H. Meyer, Dynamics of density equilibration near the liquid-vapor critical point of He-3, Czechoslovak J. Phys. 46, Suppl. 1, 71-72 (1996)
18. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed., Pergamon, Oxford, 1987
19. F. B. Lipps and R. S. Hemler, A scale analysis of deep moist convection and some related numerical calculations, J. Atmos. Sci. 39, 2192-2210 (1982)
20. A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, Vol. 53, Springer, New York, 1984
21. A. Majda and J. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion, Combust. Sci. Tech. 42, 185-205 (1985)
22. M. R. Moldover, J. V. Sengers, R. W. Gammon, and J. R. Hocken, Gravity effects in fluids near the gas-liquid critical point, Rev. Mod. Phys. 51, 79-99 (1979)
23. Y. Ogura and N. A. Phillips, Scale analysis of deep and shallow convection in the atmosphere, J. Atmos. Sci. 19, 173-179 (1962)
24. A. Onuki and R. A. Ferrell, Adiabatic heating effect near the gas-liquid critical point, Physica A 164, 245-264 (1990)
25. A. Onuki, H. Hao, and R. A. Ferrell, Fast adiabatic equilibration in a single-component fluid near the liquid-vapor critical point, Phys. Review A 41, 2256-2259 (1990)
26. V. A. Rabinovich, Thermophysical Properties of Neon, Argon, Krypton, and Xenon, Hemisphere Publishing Corp., New York, 1988
27. R. G. Rehm and H. R. Baum, The equations of motion for thermally driven, buoyant flows, J. Res. Natl. Bur. Stand. 83, 297-308 (1973)
28. J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity, Clarendon Press, Oxford, 1982
29. J. V. Sengers, Transport properties of fluids near critical points, Internat. J. Thermophysics 6, 203-232 (1985)
30. J. V. Sengers, R. S. Basu, and J. M. H. Levelt Sengers, Representative equations for the thermodynamic and transport properties of fluids near the gas-liquid critical point, NASA Contractor Report 3424, 1981
31. H. L. Swinney and D. L. Henry, Dynamics of fluids near the critical point: Decay rate of order-parameter fluctuations, Phys. Rev. A 8, 2586-2617 (1973), and references therein
32. R. Wilhelmson and Y. Ogura, The pressure perturbation and the numerical modeling of a cloud, J. Atmos. Sci. 29, 1295-1307 (1972)
33. C.-S. Yih, Stratified Flows, Academic Press, New York, 1980
34. B. Zappoli and P. Carles, The thermo-acoustic nature of the critical speeding up, Eur. J. Mech. B/Fluids 14, 41-65 (1995)
35. B. Zappoli, S. Amiroudine, P. Carlès, and J. Ouazzani, Thermoacoustic and buoyancy-driven transport in a square side heated cavity filled with a near critical fluid, J. Fluid Mech. 316, 53-72 (1996)
36. F. Zhong and H. Meyer, Density equilibration near the liquid-vapor critical point of a pure fluid: Single phase, Phys. Rev. E 51 3223-3241 (1995)