Lattice-Boltzmann accuracy in pore-scale flow simulation

We investigate the possibility of using nominally second-order-accurate techniques for resolving flow about solid boundaries as a means of improving accuracy and reducing grid resolution requirements in pore-scale simulations. An LBGK method is used to calculate flow in several geometries of increasing complexity, using a first-order accurate and two nominally second-order-accurate methods for no-slip boundaries. The geometries include uniform flow past an isolated sphere, quadratic flow past a sphere near a wall, flow through a BCC array of spheres, and through a randomly packed bed of spheres. The packed bed flows are also used to compare hydrodynamic dispersion results. The results confirm second-order-accurate behavior where Navier–Stokes flows are clearly developed. However 3D pore-scale simulations involve a trade-off between resolution of the flow and the number of pore spaces, and there is a resolution threshold, below which certain flow features, such as recirculation, are not resolved. We conjecture that most simulations will tend to operate near this threshold because of the competing demands for resolution and statistical accuracy. We consider local flow features and the velocity distribution, in addition to hydraulic permeability and drag, to provide a fuller understanding of accuracy near this threshold.