Abstract
An approach to numerically integrate the Landau-Lifshitz fluctuating hydrodynamic equations is outlined. The method is applied to one-dimensional systems obeying the nonlinear Fourier equation and the full hydrodynamic equations for a dilute gas. Static spatial correlation functions are obtained from computer-generated sample trajectories (time series). They are found to show the emergence of long-range behavior whenever a temperature gradient is applied. The results are in very good agreement with those obtained from solving the correlation equations directly.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Special issue devoted to Nonequilibrium Fluids,Physica 118A (1983).
L. D. Landau and E. M. Lifshitz,Fluid Mechanics (Pergamon Press, Oxford, 1984).
M. H. Ernst and E. G. D. Cohen,J. Stat. Phys. 25:153 (1981).
I. Procaccia, D. Ronis, and I. Oppenheim,Phys. Rev. Lett. 42:287 (1979); D. Ronis, I. Procaccia, and I. Oppenheim,Phys. Rev. A 19:1324 (1979); D. Ronis and S. Putterman,Phys. Rev. A 22:773 (1980).
A.-M. S. Tremblay, M. Arai, and E. Siggia,Phys. Rev. A 23:1451 (1981).
G. Van Der Zwan, D. Bedaux, and P. Mazur,Physica 107A:491 (1981).
T. R. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman,Phys. Rev. Lett. 44:472 (1980).
T. R. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman,Phys. Rev. Lett. 42:862 (1979).
J. Dufty, inSpectral Line Shapes, P. Wende, ed. (de Gruyer, Berlin, 1981), p. 1143.
D. Beysens, Y. Garrabos, and G. Zalczer,Phys. Rev. Lett. 45:403 (1980); R. Penney, H. Kiefte, and J. M. Clouter,Bull. Can. Assoc. Phys. 39:BB8 (1983).
G. Wegdam, N. M. Van Keulen, and J. C. F. Michielsen,Phys. Rev. Lett. 55:630 (1985).
T. R. Kirkpatrick and E. G. D. Cohen,Phys. Lett. 78A:350 (1980); D. Ronis and I. Procaccia,Phys. Rev. A 26:1812 (1982).
G. Satten and D. Ronis,Phys. Rev. A 26:940 (1982); T. R. Kirkpatrick and E. G. D. Cohen,Phys. Rev. A 26:972 (1982).
A. M. Tremblay, inRecent Developments in Nonequilibrium Thermodynamics, J. Casas-Vasquez, D. Jou, and G. Lebon, eds. (Springer-Verlag, Berlin, 1984).
M. Mareschal and E. Kestemont,Phys. Rev. A 30:1158 (1984).
A. Garcia,Phys. Rev. A 34:1454 (1986).
M. Malek Mansour, A. L. Garcia, G. C. Lie, and E. Clementi,Phys. Rev. Lett. 58:874 (1987).
L. Arnold,Stochastic Differential Equations: Theory and Applications (Wiley, New York, 1974).
M. Malek Mansour, J. W. Turner, A. L. Garcia, M. Mareschal, and G. Nicolis, in preparation.
B. Berne and R. Pecora,Dynamic Light Scattering (Wiley, New York, 1976).
T. G. Kurtz,Math. Prog. Study 5:67 (1976);Huston J. Math. 3:67 (1977);Stoch. Proc. Appl. 6:223 (1978).
C. VanDen Broeck, M. Malek Mansour, and F. Baras,J. Stat. Phys. 28:557 (1982).
J. Perez-Madrid and J. M. Rubi,Phys. Rev. A 33:2716 (1986).
L. Arnold and R. Lefever, eds.,Stochastic Nonlinear Systems in Physics, Chemistry and Biology (Springer, Berlin, 1981); J. W. Duffy, J. J. Brey, and M. C. Marchetti,Phys. Rev. A 33:4307 (1986).
G. Nicolis and M. Malek Mansour,Phys. Rev. A 29:2845 (1984).
W. Rumelin,SIAM J. Numer. Anal. 19:604 (1982).
M. Abramowitz and I. Stegun,Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1972), Eq. 25.3.27.
P. Resibois and M. DeLeener,Classical Kinetic Theory of Fluids (Wiley, New York, 1977).
R. Schmilz and E. G. D. Cohen,J. Stat. Phys. 38:285 (1985).
J. Lutsko and J. W. Dufty,Phys. Rev. A 32:3040 (1985).
G. Nicolis and I. Prigogine,Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977).
M. Malek Mansour, C. Van Den Broeck, G. Nicolis, and J. W. Turner,Ann. Phys. (N.Y.) 131:283 (1981).
N. G. Van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Garcia, A.L., Mansour, M.M., Lie, G.C. et al. Numerical integration of the fluctuating hydrodynamic equations. J Stat Phys 47, 209–228 (1987). https://doi.org/10.1007/BF01009043
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01009043