Simulation of buoyancy-driven flows in a vertical cylinder using a simple lattice Boltzmann model

Axisymmetric thermal flow is of fundamental interest and practical importance. However, the work to design suitable and efficient lattice Boltzmann models on axisymmetric thermal flows is quite rare. In order to bridge the gap, a simple lattice Boltzmann model for axisymmetric thermal flow is proposed in this paper. In the present study, we show how to transform the governing equation for temperate field in the cylindrical coordinate system to the pseudo-Cartesian representation in the same way as that for the flow field. Therefore the flow field and the temperature field both are solved by the two-dimensional five-speed (D2Q5) lattice Boltzmann model. The treatment of the "geometrical forcing" due to the coordinate transformation and the physical forcing due to the temperature field is simpler than that in all existing models. Thanks to its intrinsic features, the present model is more efficient, more stable, and much simpler than the existing models. In this paper, several kinds of nontrivial thermal buoyancy-driven flows in vertical cylinders, which are of interest from the standpoint of both basic fluid dynamics and practical applications, are simulated by the present model.