Turbulent natural convection in enclosed cavities can be found in applications such as cooling and drying, nuclear reactor components, solar manifolds, and internal cooling of gas turbine blades. To simulate such flows, a finite difference lattice Boltzmann method based solver is developed in general curvilinear coordinates, first for two-dimensional flows and thereafter extended to three-dimensional flows. The developed solver is validated for natural convection in square and circular-annular-cavities over a range of Rayleigh numbers. The circular-annular-cavity is found to have laminar flow for Rayleigh numbers in the range of 10^3 –10^6, and it becomes unsteady and chaotic from 10^7 onward. The instantaneous and time-average contours of isotherms and streamlines were used to study the unsteady behavior of the flow. A universal near-wall velocity profile is found to exist in all the unsteady natural convection studies in the annular cavity case. The present results indicate that the developed solver can be successfully used to simulate natural convection in enclosed cavities. Efforts are underway to validate the three-dimensional solver with an eddy-resolving turbulence model for stationary and rotating enclosed cavities.