A study of the upper limit of solid scatters density for gray Lattice Boltzmann Method

The upper limit of the solid scatters density n(s) (x), a key parameter for the simulation of flows in porous media with a gray Lattice Boltzmann Method, is studied by an analytical way for the infiltration Poiseuille flow between two infinite parallel plates. Analyses of three different gray Lattice Boltzmann schemes, separately proposed by Gao and Sharma et al., Dardis and McCloskey, and Thorne and Sukop, indicate that the effective domain of Gao and Sharma's scheme is restricted to n(s) < 1/2 root 3 approximate to 0.289, Dardis and McCloskey's scheme is restricted to ns < (root 57-1)/28 approximate to 0.234, and that there is no extra restriction on ns (x) with Thorne and Sukop's scheme. These results are obtained for the dimensionless relaxation time tau = 1. The above analytical results are verified by our numerical simulations. The use of a gray LBM is further illustrated by simulating the flow at the interface of a porous medium. Simulation results yield velocity profiles which agree very well with Brinkman's prediction.