Simulation of turbulent natural convection in annular cavity using a high-order compact finite-difference LBM

In the present work, compact finite-difference lattice Boltzmann method is extended to simulate thermal flows using double distribution approach. Fourth-order accurate spatial and temporal discretization schemes are utilized in order to accurately simulate the flow fields. The developed solver is validated by simulating natural convection in a square cavity at Rayleigh numbers 106 and 108. Thereafter, natural convection in a circular annulus is studied for a Rayleigh number of 108. Streamlines and isotherms are used in order to visualize the results and the variation of Nusselt number and temperature profiles are studied within the cavity.