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An evaluation of lattice Boltzmann schemes for porous medium flow simulation. (English) Zbl 1177.76323
Summary: We quantitatively evaluate the capability and accuracy of the lattice Boltzmann equation (LBE) for modeling flow through porous media. In particular, we conduct a comparative study of the LBE models with the multiple-relaxation-time (MRT) and the Bhatnagar-Gross-Krook (BGK) single-relaxation-time (SRT) collision operators. We also investigate several fluid-solid boundary conditions including: (1) the standard bounce-back (SBB) scheme, (2) the linearly interpolated bounce-back (LIBB) scheme, (3) the quadratically interpolated bounce-back (QIBB) scheme, and (4) the multi-reflection (MR) scheme. Three-dimensional flow through two porous media-a body-centered cubic (BCC) array of spheres and a random-sized sphere-pack-are examined in this study. For flow past a BCC array of spheres, we validate the linear LBE model by comparing its results with the nonlinear LBE model. We investigate systematically the viscosity-dependence of the computed permeability, the discretization error, and effects due to the choice of relaxation parameters with the MRT and BGK schemes. Our results show unequivocally that the MRT-LBE model is superior to the BGK-LBE model, and interpolation significantly improves the accuracy of the fluid-solid boundary conditions.

##### MSC:
 76M28 Particle methods and lattice-gas methods 76S05 Flows in porous media; filtration; seepage
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