Hybrid LBGK-FD Model for Studying Turbulent Natural Convection

hybrid mesomacroscopic approach has been developed for modeling developed turbulent thermogravitational flows in closed rectangular differentially heated regions. Within the framework of the formulated approach, it is proposed to use the mesoscopic lattice Boltzmann equations to describe gas-dynamical processes, and the macroscopic energy equation solved by the finite difference method for thermodynamic ones. To approximate the Boltzmann equation, simultaneous relaxation and a two-dimensional nine-speed scheme were used. Mathematical simulation was carried out at the Rayleigh number Ra = 10 10 and the Prandtl number Pr = 0.71. The influence of the order of approximation of the energy equation on the local heat transfer characteristics has been analyzed. It is found that an increase in the number of computational nodes leads to the smoothing of pulsations in the flow. In this case, the results of numerical simulation agree satisfactorily with the “reference” data obtained by other researchers.