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.

Pore-scale permeability prediction for Newtonian and non-Newtonian fluids

“…Previous studies have also observed this convergence with increasing resolution, albeit not always from above (e.g., Zakirov and Galeev, 2019). Similar behavior has also been observed in Lattice-Boltzmann method (LBM) simulations (e.g., Khirevich et al, 2015;Khirevich and Patzek, 2018).…”

“…Furthermore, sandstone is known to be an ideal reservoir rock and is of certain interest for several geological fields, especially in exploration geology. Laboratory measurements of the given sample with porosity ≈ 15.2 % result in a permeability value of ≈ 1100 mD (Keehm, 2003).…”

“…It is a powerful tool which allows to improve the understanding of both pore-scale processes and rock properties. DRP approaches use 2-D or 3-D microstructural images to compute fluid flows (Fredrich et al, 1993;Ferreol and Rothman, 1995;Keehm, 2003;Bosl et al, 1998), which are obtained using modern techniques including X-ray computed tomography (CT) and nuclear magnetic resonance imaging (NMR) (Dvorkin et al, 2011;Arns et al, 2001;Arns, 2004). In a first step, the obtained microstructural images undergo several stages of segmentation (binarization, smoothing, etc.…”

“…The subsequent computation of fluid flow through the reconstructed three-dimensional pore space is tackled with either Lattice-Boltzmann (Bosl et al, 1998;Pan et al, 2004;Guo and Zhao, 2002), finite difference (Manwart et al, 2002;Shabro et al, 2014;Gerke et al, 2018) or finite element methods (Garcia et al, 2009;Akanji and Matthai, 2010;Bird et al, 2014). The computed velocity field is then used to estimate permeability (Keehm, 2003;Saxena et al, 2017) and other physical properties (Saxena and Mavko, 2016;Knackstedt et al, 2009).…”

A coupled lattice Boltzmann method and discrete element method for discrete particle simulations of particulate flows

“…Once converged, we can evaluate the force acting on the sphere and compare it against existing quasi-analytical solutions [48]. Due to its simplicity and the existence of a quasi-analytical solution, it is a well-studied setup, both for classical DNS approaches [49] as well as for the LBM [39,41,27,50]. For LBM simulations, this is a particularly important test as some collision operators suffer from an undesired dependence of the drag force on the relaxation rate s ν , which affects the simulated boundary location [39].…”