New form of governing equations of fluids arising from Hamilton's principle

International Journal of Engineering Science

Volumn 37, Issue 12, 1999, Pages 1495-1520

  Gavrilyuk, S ^a   Gouin, H ^a  

^a AIX MARSEILLE UNIVERSITY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; EQUATIONS OF STATE OF LIQUIDS; MATRIX ALGEBRA;

GODUNOV-FRIEDRICHS-LAX EQUATION; HAMILTON'S PRINCIPLE;

FLUID DYNAMICS;

EID: 0033196934     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7225(98)00131-1     Document Type: Article

References (22)

1. L.I. Sedov, Mathematical methods for constructing new models of continuum media, Uspekhi Mat. Nauk. 20 (1965) 121-180 (in Russian).
2. J. Serrin, Mathematical principles of classical fluid mechanics, Encyclopedia of Physics VIII/1, Springer, Berlin, 1959, pp. 125-263.
3. V.L. Berdichevsky, Variational Principles of Continuum Mechanics, Nauka, Moscow, 1983 (in Russian).
4. Godunov S.K. An interesting class of quasilinear systems. Sov. Math. Dokl. 2:1961;947-949.
5. Friedrichs K.O., Lax P.D. Systems of conservation laws with a convex extension. Proc. Nat. Acad. Sci. USA. 68:1971;1686-1688.
6. P. Casal, H. Gouin, Equations of motions of thermocapillary fluids, C.R. Acad. Sci. Paris 306 (II) (1988) 99-104.
7. Slemrod M. Dynamic phase transitions in a van der Waals fluid. J. Differential Equations. 52:1984;1-23.
8. van Wijngaarden L. On the equations of motions for mixture of liquid and gas bubbles. J. Fluid Mech. 33:1972;465-474.
9. Bedford A., Drumheller D.S. Theories of immiscible and structured mixtures. Int. J. Engng. Sci. 21:1983;863-1018.
10. Gavrilyuk S.L., Shugrin S.M. Media with equations of state that depend on derivatives. J. Appl. Mech. Techn. Phys. 37:1996;179-189.
11. S. K. Godunov, E.I. Romensky, Thermodynamics, conservation laws and symmetric forms of differential equations in mechanics of continuous media, in: M. Hafez, K. Oshima (Eds.), Computational Fluid Dynamics Review, Willey, New York, 1995, pp. 19-30.
12. G. Boillat, Non-linear hyperbolic fields and waves, in: T. Ruggeri (Ed.), Recent Mathematical Methods in Nonlinear Wave Propagation, Springer, Berlin, 1996, pp. 1-47.
13. L.V. Ovsyannikov, Lectures on the Gas Dynamics Foundations, Nauka, Moscow, 1981 (in Russian).
14. D. Serre, Systèmes de Lois de Conservation I, II, Diderot Editeur, Arts et Sciences, Paris, 1996.
15. S.L. Gavrilyuk, H. Gouin, Yu.V. Perepechko, A variational principle for two-fluid models, C.R. Acad. Sci. Paris 324 (IIb) (1997) 483-490.
16. Gavrilyuk S.L., Gouin H., Perepechko Yu.V. Hyperbolic models of two-fluid mixtures. Meccanica. 33:1998;161-175.
17. Gouin H., Gavrilyuk S.L. Hamilton's principle and Rankine-Hugoniot conditions for general motions of mixtures. Meccanica. 33:1998.
18. Geurst J.A. Virtual mass in two-phase bubbly flow. Physica A. 129:1985;233-261.
19. Geurst J.A. Variational principles and two-fluid hydrodynamics of bubbly liquid/gas mixtures. Physica A. 135:1986;455-486.
20. Gouin H. Variational theory of mixtures in continuum mechanics. Eur. J. Mech. B/Fluids. 9:1990;469-491.
21. S.L. Gavrilyuk, Yu.V. Perepechko, Variational approach for the construction of hyperbolic two-fluid models, Zh. Prikl. Mekh. Tekh. Fiz. 39 (5) (1998) 39-54 (in Russian).
22. T.C. Haley, R.T. Lahey Jr., D.A. Drew, A characteristic analysis of void waves using two-fluid models, Proceedings of the International Conference on Multiphase Flows'91 - Tsukuba, 24-27 September, Tsukuba, Japan, 1991, pp. 161-164.