Behavior of numerical error in pore-scale lattice Boltzmann simulations with simple bounce-back rule: Analysis and highly accurate extrapolation
KAUST DepartmentAli I. Al-Naimi Petroleum Engineering Research Center (ANPERC)
Energy Resources and Petroleum Engineering
Physical Science and Engineering (PSE) Division
Online Publication Date2018-09-14
Print Publication Date2018-09
Permanent link to this recordhttp://hdl.handle.net/10754/628723
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AbstractWe 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.
CitationKhirevich S, Patzek TW (2018) Behavior of numerical error in pore-scale lattice Boltzmann simulations with simple bounce-back rule: Analysis and highly accurate extrapolation. Physics of Fluids 30: 093604. Available: http://dx.doi.org/10.1063/1.5042229.
SponsorsWe are grateful for the allocation of computational resources by the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia.
JournalPhysics of Fluids