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A cascaded lattice Boltzmann (LB) approach based on central moments andmultiple relaxation times to simulate thermal convective flows, which aredriven by buoyancy forces and/or swirling effects, in the cylindricalcoordinate system with axial symmetry is presented. In this regard, thedynamics of the axial and radial momentum components along with the pressureare represented by means of the 2D Navier-Stokes equations with geometric massand momentum source terms in the pseudo Cartesian form, while the evolutions ofthe azimuthal momentum and the temperature field are each modeled by anadvection-diffusion type equation with appropriate local source terms. Based onthese, cascaded LB schemes involving three distribution functions areformulated to solve for the fluid motion in the meridian plane using a D2Q9lattice, and to solve for the azimuthal momentum and the temperature field eachusing a D2Q5 lattice. The geometric mass and momentum source terms for the flowfields and the energy source term for the temperature field are included usinga new symmetric operator splitting technique, via pre-collision andpost-collision source steps around the cascaded collision step for eachdistribution function. These result in a particularly simple and compactformulation to directly represent the effect of various geometric source termsconsistently in terms of changes in the appropriate zeroth and first ordermoments. Simulations of several complex buoyancy-driven thermal flows andincluding rotational effects in cylindrical geometries using the newaxisymmetric cascaded LB schemes show good agreement with prior benchmarkresults for the structures of the velocity and thermal fields as well as theheat transfer rates given in terms of the Nusselt numbers.

Cascaded Lattice Boltzmann Method based on Central Moments for Axisymmetric Thermal Flows Including Swirling Effects