Behavior of numerical error in pore-scale lattice Boltzmann simulations with simple bounce-back rule: Analysis and highly accurate extrapolation

Abstract

We perform the viscosity-independent Stokes flow simulations in regular sphere packings using the two-relaxation-times (TRT) lattice Boltzmann method (LBM) with the simple bounce-back (BB) rule. Our special discretization procedure reduces the scatter in integral quantities, such as drag force, and quantifies the solution convergence error. We assume transition to linear (−1) convergence rate for different sets of TRT parameters and use this assumption to provide a simple extrapolation scheme. After establishing the accurate reference values of drag for a wide range of porosities, 0.26–0.78, we show a ten-fold decrease in the drag error using the suggested extrapolations. This error decrease allows the simple LBM/BB scheme to reach an accuracy of the high-order interpolated boundary schemes. The suggested extrapolation approach is straightforward to apply in porous media, whose pore space can be discretized at several resolutions.