Two-Dimensional Lattice Boltzmann for Reactive Rayleigh-Bénard and Bénard-Poiseuille Regimes

We perform a computer simulation of the reaction-diffusion and convection that takes place in Rayleigh–Bénard and Bénard–Poiseuille regimes. The lattice Boltzmann equation (LBE) is used along with the Boussinesq approximation to solve the non-linear coupled differential equations that govern the systems’ thermo-hydrodynamics. Another LBE, is introduced to calculate the evolution concentration of the chemical species involved in the chemical reactions. The simulations are conducted at low Reynolds numbers and in terms of steady state between the first and second thermo-hydrodynamics instability. The results presented here (with no chemical reactions) are in good agreement with those reported in the scientific literature which gives us high expectations about the reliability of the chemical kinetics simulation. Some examples are provided.