Lattice Boltzmann Method for Computing 3D Navier-Stokes Equations in Orthogonal Curvilinear Coordinates: Flow Simulations using Clustered and Body-Conforming Grids

The use of clustered grids that adapt with the nature of multiscale flows and the body-fitted grids for flow over curved geometries greatly facilitate efficient flow simulations. The standard lattice Boltzmann (LB) methods, however, use uniform Cartesian grids and implement conditions on the boundaries via cut-cell approaches. We develop improved LB methods that accommodate both these aspects naturally by constructing equilibria and body forces via using a Chapman-Enskog analysis that recover the 3D Navier-Stokes equations in orthogonal curvilinear coordinates (OCC) in a computational space using the D3Q27 lattice. The presence of variable grids or curved boundaries in the physical space are represented via the OCC related metric factors and a tensor associated with their spatial derivatives in the LB collision operator. This significantly extends our recent work on the 2D OCC-LBM (Yahia & Premnath, 2024) and uses our Fokker-Planck central moment-based collision model (Schupbach & Premnath, 2024) for further improvements in stability for flow simulations using OCC. The method is modular in nature and maintains the simplicity of the collide-and-stream steps. Simulations of various 3D benchmark flow cases demonstrate the capabilities of our 3D OCC-LBM.