Efficient Simulation of Axisymmetric Swirling Flows via a Lattice Boltzmann Method using Transformations Based on Orthogonal Coordinates

Axisymmetric flow equations represent a dimensional reduction of three-dimensional flows where axial symmetry can be exploited. If such flows involve boundary layers or shear layers, they can be more efficiently resolved by the clustering of grids that follow the flow features. However, the standard lattice Boltzmann (LB) methods are generally restricted to uniform Cartesian grids. To overcome this limitation, we develop a new LB method that solves the axisymmetric Navier-Stokes equations based on general orthogonal coordinates in a computational domain. We construct a collision model whose equilibria as well as the geometric body forces depend on the metric coefficients and their spatial derivatives arising from the variable grids used in the physical domain. The swirl effects in such flows are accounted for by computing the azimuthal momentum that satisfies a convection-diffusion type equation with a source term in general orthogonal coordinates using another LB scheme. Both these LB methods are designed to accommodate the usual collide-and-stream steps while still effectively allowing the use of variable grids, and their collision operators are based on central moments. We show the efficacy of our approach for various canonical axisymmetric flows including swirl effects.