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

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. (c) 2012 Elsevier Ltd. All rights reserved.