Lattice-Boltzmann simulations in reconstructed parametrized porous media

Abstract

Computations of flows in explicitly resolved porous media reported in the literature so far are based on binarized porous media data mapped to uniform Cartesian grids. The voxel set is directly being used as the computational grid and thus the geometrical representation is usually only first-order accurate due to stair-case patterns. In this work, we pursue a more elaborate approach: starting from a highly resolved tomographic grey value data set we utilize a Marching Cube algorithm to reconstruct the surface of the porous medium as a set of planar triangles. The numerical resolution of the Cartesian grid for the simulation can then be chosen independently from the voxel set. As we take into account the subgrid distances between the nodes of the Cartesian grid and the planar triangle surfaces, one can utilize a second-order accurate lattice Boltzmann flow solver to efficiently compute, e.g. permeabilities. As these interpolation-based no-slip boundary conditions are not mass preserving, we also present a local modification of the no-slip boundary condition restoring mass conservation. Our numerical results demonstrate that for saturated flow simulations this coupled approach allows a substantial acceleration of saturated flow computations in porous media.