Analysis and improvement of Brinkman lattice Boltzmann schemes: bulk, boundary, interface. Similarity and distinctness with finite elements in heterogeneous porous media

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Irina GinzburgLaurent Talon

Abstract

This work focuses on the numerical solution of the Stokes-Brinkman equation for a voxel-type porous-media grid, resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude. It is first analytically demonstrated that the lattice Boltzmann method (LBM) and the linear-finite-element method (FEM) both suffer from the viscosity correction induced by the linear variation of the resistance with the velocity. This numerical artefact may lead to an apparent negative viscosity in low-permeable blocks, inducing spurious velocity oscillations. The two-relaxation-times (TRT) LBM may control this effect thanks to free-tunable two-rates combination Λ. Moreover, the Brinkman-force-based BF-TRT schemes may maintain the nondimensional Darcy group and produce viscosity-independent permeability provided that the spatial distribution of Λ is fixed independently of the kinematic viscosity. Such a property is lost not only in the BF-BGK scheme but also by "partial bounce-back" TRT gray models, as shown in this work. Further, we propose a consistent and improved IBF-TRT model which vanishes viscosity correction via simple specific adjusting of the viscous-mode relaxation rate to local permeability value. This prevents th...Continue Reading

References

Oct 9, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zhaoli Guo, T S Zhao
Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Qinjun KangShiyi Chen
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Irina Ginzburg, Dominique d'Humières
Oct 11, 2005·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dominique D'HumièresLi-Shi Luo
Jul 23, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Irina Ginzburg
Apr 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ngoc H PhamDimitrios V Papavassiliou
May 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Like LiJames F Klausner
Aug 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hiroaki YoshidaKenji Fukuzawa
Oct 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ruru LiCaineng Zou

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Citations

Jan 20, 2018·Physical Review. E·Gerald G PereiraShakil Ahmed
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Qiang Ma, Zhenqian Chen

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