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.
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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
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DOI: https://doi.org/10.1007/BF01009043