Three-dimensional Central Moment Lattice Boltzmann Methods based on Orthogonal Curvilinear Coordinates and Fokker-Planck Collision Models for Thermal Convective Flows

Thermal convective flows occur in a wide range of applications, e.g., from microfluidics to geophysical flows. Their multiscale nature can be more efficiently simulated using nonuniform and body-conforming grids. However, the standard lattice Boltzmann method (LBM) is based on the use of Cartesian square/cubic grids with higher computational costs. To address these, we develop novel 3D LBMs based on orthogonal curvilinear coordinates (OCC) for solving the Navier-Stokes equations coupled with the energy equation using a double distributions framework. We incorporate the recently developed Fokker-Planck central moment formulations in constructing their collision steps for enhanced numerical stability and using the D3Q27 lattice and D3Q15 lattice for the flow field and the temperature field, respectively. The central moment equilibria in the collision models are augmented with the use of OCC metric factors to accommodate the local variations in the grids. The resulting 3D OCC LBM solvers maintain the natural parallelization capabilities of the collide-and-stream steps while delivering significant improvements in computational efficiency. We show the efficacy of our approach for a benchmark study involving 3D thermal convective flows in an enclosure at high Rayleigh numbers.