  A cascaded lattice Boltzmann (LB) approach based on central moments and
multiple relaxation times to simulate thermal convective flows, which are
driven by buoyancy forces and/or swirling effects, in the cylindrical
coordinate system with axial symmetry is presented. In this regard, the
dynamics of the axial and radial momentum components along with the pressure
are represented by means of the 2D Navier-Stokes equations with geometric mass
and momentum source terms in the pseudo Cartesian form, while the evolutions of
the azimuthal momentum and the temperature field are each modeled by an
advection-diffusion type equation with appropriate local source terms. Based on
these, cascaded LB schemes involving three distribution functions are
formulated to solve for the fluid motion in the meridian plane using a D2Q9
lattice, and to solve for the azimuthal momentum and the temperature field each
using a D2Q5 lattice. The geometric mass and momentum source terms for the flow
fields and the energy source term for the temperature field are included using
a new symmetric operator splitting technique, via pre-collision and
post-collision source steps around the cascaded collision step for each
distribution function. These result in a particularly simple and compact
formulation to directly represent the effect of various geometric source terms
consistently in terms of changes in the appropriate zeroth and first order
moments. Simulations of several complex buoyancy-driven thermal flows and
including rotational effects in cylindrical geometries using the new
axisymmetric cascaded LB schemes show good agreement with prior benchmark
results for the structures of the velocity and thermal fields as well as the
heat transfer rates given in terms of the Nusselt numbers.
