Phase transition in Van Der Waals fluid

SIAM Journal on Applied Mathematics

Volumn 57, Issue 4, 1997, Pages 871-892

  Hsieh, Din Yu ^a   Wang, Xiao Ping ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Phase transition; Stability; Van der Waals fluid

Indexed keywords

FLUIDS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY; VISCOSITY;

PSEUDOSPECTRAL METHOD; VAN DER WAALS FLUID; VAN DER WAALS SYSTEM;

PHASE TRANSITIONS;

EID: 0031210805     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139995295165     Document Type: Article

References (24)

1. M. AFFOUF AND R. CAFLISCH, A numerical study of Riemann problem solutions and stability for a system, of viscous conservation laws of mixed type, SIAM J. Appl. Math., 51 (1991), pp. 605-634.
2. N. ALIKAKOS, P.W. BATES, AND G. FUSCO, Slow motion for the Cahn-Hilliard equation in one space dimension, J. Differential Equations, 90 (1991), pp. 81-135.
3. P.W. BATES AND P.C. FIFE, The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math., 53 (1993), pp. 990-1008.
4. P.W. BATES AND J. XUN, Metastable patterns for the Cahn-Hilliard equation. II. Layer dynamics and slow invariant manifold, J. Differential Equations, 117 (1995), pp. 165-216.
5. L. BRONSARD AND R. KOHN, On the slowness of phase boundary motion in one space dimension, Comm. Pure Appl. Math., 43 (1990), pp. 983-998.
6. J. CARR, M. GURTIN, AND M. SLEMROD, Structured phase transitions on a finite interval, Arch. Rational Mech. Anal., 86 (1984), pp. 317-351.
7. B. COCKBURN AND H. GAU, A model numerical scheme for the propagation of phase transitions in solids, SIAM J. Sci. Comp., 17 (1996), pp. 1092-1121.
8. C. DAFERMOS, Admissible wave fans in nonlinear hyperbolic systems, Arch. Rational Mech. Anal., 106 (1989), pp. 243-260.
9. H.T. FAN, A limiting "viscosity" approach to the Riemann problem for materials exhibiting a change of phase. II. Arch. Rational Mech. Anal., 116 (1992), pp. 317-337.
10. E. FERMI, Thermodynamics, Dover, New York, 1956.
11. M.E. GURTIN, On phase transitions with bulk, interfacial, and boundary energy, Arch. Rational Mech. Anal., 96 (1986), pp. 243-264.
12. D. HOFF AND M. KHODJA, Stability of coexisting phases for compressible van der Waals fluids, SIAM J. Appl. Math., 53 (1993), pp. 1-14.
13. S. JIN, Numerical integrations of systems of conservation laws of mixed type, SIAM J. Appl. Math., 55 (1995), pp. 1536-1551.
14. T.-P. LIU, Nonlinear stability of shock waves for viscous conservation laws, Memoirs Amer. Math. Soc., 328 (1986).
15. L. MODICA, The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal., 98 (1987), pp. 123-142.
16. R.L. PEGO, Front migration in the nonlinear Cahn-Hilliard equation, Proc. Roy. Soc. London Ser. A, 422 (1989), pp. 261-278.
17. M. SHEARER, The Riemann problem for a class of conservation laws of mixed type, J. Differential Equations, 46 (1982), pp. 426-443.
18. C.W. SHU, A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting, J. Comp. Phys., 100 (1992), pp. 424-429.
19. M. SLEMROD, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 81 (1983), pp. 301-315.
20. M. SLEMROD AND J.E. FLAHERTY, Numerical integration of a Riemann problem for a Van Der Waals fluid, in Phase Transformation, C.A. Elias and G. John, eds., Elsevier, New York, 1986.
21. M. SLEMROD, A limiting "viscosity" approach to the Riemann problem for materials exhibiting change of phase, Arch. Rational Mech. Anal., 105 (1989), pp. 327-365.
22. A. SZEMPESSY AND Z. XIN, Nonlinear stability of viscous shock waves, Arch, Rational Mech. Anal., 122 (1993), pp. 53-103.
23. S.Q. TANG, Dissipative Nonlinear Evolution Equations and Chaos, Ph.D. thesis, Hong Kong University of Science and Technology, 1995.
24. X.P. WANG, S.Q. TANG, L.X. Wu, AND D.Y. HSIEH, Complexities Arising from the Study of a Nonlinear Evolution System with Small Dissipation, Technical report 95-3-1, Dept. of Math., Hong Kong University of Science and Technology,