On the Finite Difference-Based Lattice Boltzmann Method in Curvilinear Coordinates

The lattice Boltzmann method is a microscopic-based approach for solving the fluid flow problems at the macroscopic scales. The presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility. To circumvent such difficulties, a finite difference-based lattice Boltzmann method (FDLBM) in curvilinear coordinates is explored using body-fitted coordinates with non-uniform grids. Several test cases, including the impulsively started cylindrical Couette flow, steady state cylindrical Couette flow, steady flow over flat plates, and steady flow over a circular cylinder, are used to examine various issues related to the FDLBM. The effect of boundary conditions for the distribution functions on the solution, the merits between second-order central difference and upwind schemes for advection terms, and the effect of the Reynolds number are investigated. Favorable results are obtained using FDLBM in curvilinear coordinates, indicating that the method is potentially capable of solving finite Reynolds number flow problems in complex geometries.