Fig. 15-2 Velocity vector (top) and temperature distribution (bottom) at the steady state with a Rayleigh number of 3414 Stable convection rolls and a corresponding temperature field are established when the Rayleigh number exceeds the critical value (1708). The downward and upward flows, respectively, are found at the center and side of the flow field (top). It is seen that a cold region is expanded downward at the center.

Fig. 15-3 Change in temperature distribution due to the Rayleigh number The critical Rayleigh number, at which a temperature bifurcation appears, agrees with that obtained by linear theory.

As one of the research items of "Computational Science Research in Nuclear Fields", the Rayleigh-benard system, where a fluid is heated from below and cooled from above, is studied using molecular dynamics and direct simulation Monte Carlo methods. It is known that convection rolls appear when the Rayleigh number defined by the temperature difference between the top and bottom exeeds a critical value, while heat conduction is established when the Rayleigh number is smaller. Typical flow velocity and temperature fields obtained by the Monte Carlo method are shown in Fig. 15-2. Large and stable convection rolls are observed because of the sufficiently high Rayleigh number. The mid-elevation temperatures are shown in Fig. 15-3. A temperature bifurcation due to the onset of convection is found at around a Rayleigh number of 1700. Although the critical Rayleigh number is obtained as 1708 from the linear stability analysis of hydrodynamic equations, it is shown for the first time that the same critical Rayleigh number is obtained by a molecular-level simulation.

Reference T. Watanabe et al., Simulation of a Two-Dimensional Rayleigh-Benard System Using the Direct Simulation Monte Carlo Method, Phys. Rev., E 49, 4060 (1994).

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