Lattice Bhatnagar--Gross--Krook Simulations of Hydromagnetic Double-Diffusive Convection in a Rectangular Enclosure with Opposing Temperature and Concentration Gradients

The temperature-concentration lattice Bhatnagar--Gross--Krook (TCLBGK) model with a robust boundary scheme is developed for two-dimensional hydromagnetic double-diffusive convective flow of a binary gas mixture in a rectangular enclosure, in which the upper and lower walls are insulated, while the left and right walls are constant temperature and constant concentration, and a uniform magnetic field is applied in the x-direction. In the model the velocity, temperature and concentration fields are solved by three independent LBGK equations, which are combined into a coupled equation for the whole system. In our simulations, we take the Prandtl number Pr=1.0, the Lewis number Le=2.0, the thermal Rayleigh number Ra_T=10⁵, and the aspect ratio A=2 for the enclosure. The numerical results are found to be in good agreement with those of previous studies.