Simulation of three-dimensional convection pattern in a Rayleigh-Bénard system using the direct simulation Monte Carlo method

Abstract

The Rayleigh-Benard (RB) system, in which a fluid is contained between two horizontal parallel walls and the bottom wall is kept at a higher temperature than the wall, is one of the most representative nonequilibrium hydrodynamic systems. In the RB system, a heat conduction state is established when the temperature difference between the top and bottom walls is smaller than a critical value, while convection rolls appear when the temperature difference exceeds the critical value. Experimental and numerical studies have been conducted extensively on convection in the RB system. In recent years, the RB convection has been studied at the molecular level using the particle simulation method such as the direct simulation Monte Carlo (DSMC) method, in which a smaller number of representative particles simulates a large number of molecules in a real gas. The trajectories of the particles are traced in a short time interval by decoupling inter-particle collisions, which take place on a probabilistic basis. This chapter goes in depth of the DSMC method that is applied to simulate the RB system in a 3D rectangular box with an aspect ratio of 2: 2: 1. The side length of a sampling cell, in which the collision process is calculated, is smaller than the mean free path. The DSMC program is parallelized and the simulations are performed on Intel Paragon XP/S75, using 256 PEs with a memory size of 128MB × 256.