Comparison of Lattice Boltzmann and Boundary Element Methods for Stokes and Visco-Inertial Flow in a Two-Dimensional Porous Medium

In porous media, limitations imposed by macroscale laws can be avoided with a dual-scale model, in which the pore-scale phenomena of interest are modelled directly over a large number of realisations. Such a model requires a robust, accurate and efficient pore-scale solver. We compare the boundary element method (BEM) and two variants of the lattice Boltzmann method (LBM) as pore-scale solvers of 2D incompressible flow. The methods are run on a number of test cases and the performance of each simulation is assessed according to the mean velocity error and the computational runtime. Both the porous geometry (porosity, shape and complexity), and the Reynolds number (from Stokes to visco-inertial flow) are varied between the test cases. We find that, for Stokes flow, BEM provides the most efficient and accurate solution in simple geometries (with small boundary length) or when a large runtime is practical. In all other situations we consider, one of the variants of LBM performs best. We furthermore demonstrate that these findings also apply in a dual-scale model of Stokes flow through a locally-periodic medium.