Lattice Boltzmann simulation of the two-dimensional Poiseuille-Rayleigh-Benard flows instability

A numerical method based on the lattice Boltzmann equation (LBE) is developed in two dimensions to solve the equations of conservation of energy and momentum of a Poiseuille-Rayleigh-Benard (PRB) mixed-flow. The configuration considered in this work is a channel heated from below, cooled from the top and crossed by a fluid (Pr = 1). The study is conducted for a range of Rayleigh numbers (0 < Ra < 5000) and Reynolds (0 < Re < 500). For Re = 0 and Ra exceeds the critical value (1707.76), the Rayleigh-Benard (RB) mixed-flow appears. However, for Re values other than 0, the transition from Poiseuille flow in a cellular flow is obtained for the largest critical Ra (in limited area) and characteristics of cells depend on the intensity of the flow at the entrance of the channel.