Lattice Boltzmann simulations of flow past a circular cylinder and in simple porous media

Abstract

The single relaxation time variant of the Lattice-Boltzmann Method (LBM) is applied to the two–dimensional simulations of viscous fluids. Two flow geometries are considered: a single obstacle (circular cylinder) and a system of obstacles making up a simple, computer-created porous medium. A comparative study of two boundary schemes at the fluid–solid interface is performed. Although reasonable results can be achieved with the usage of (non-equilibrium) half-way bounce–back conditions, the interpolation-free scheme is recommended because of its better accuracy and stability. For flow past a circular cylinder, the lift and drag coefficients are computed together with the Strouhal numbers for periodically shedding vortices and validated against empirical relationships for a wide range of Reynolds numbers. The single cylinder case was also used for a novel comparison of two outlet schemes. Next, the system of obstacles that makes up a porous medium is created in two ways: by a regular arrangement of identical obstacles and by a simple randomization of cylinder centres and radii. The pressure loss in function of volumetric flow rate is compared with empirical relationships: the Darcy–Forchheimer law and the Ergun correlation. The impact of the LBM boundary schemes and the Reynolds number on the permeability and Forchheimer coefficients is studied for the two arrangements.