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Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media

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  • Liu, Qing
  • He, Ya-Ling

Abstract

In this paper, a two-dimensional eight-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman–Forchheimer-extended Darcy model. In the model, the porosity is included into the pressure-based equilibrium moments, and the linear and nonlinear drag forces of the porous matrix are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. Through the Chapman–Enskog analysis, the incompressible generalized Navier–Stokes equations can be recovered. Numerical simulations of several typical porous flows are carried out to validate the present MRT-LB model. It is found that the present numerical results agree well with the analytical solutions and/or other numerical results reported in the literature.

Suggested Citation

  • Liu, Qing & He, Ya-Ling, 2015. "Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 215-230.
    • Handle: RePEc:eee:phsmap:v:429:y:2015:i:c:p:215-230
    DOI: 10.1016/j.physa.2015.01.067
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    References listed on IDEAS

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    1. David M. Freed, 1998. "Lattice-Boltzmann Method for Macroscopic Porous Media Modeling," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1491-1503.
    2. S. Succi, 2008. "Lattice Boltzmann across scales: from turbulence to DNA translocation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 64(3), pages 471-479, August.
    3. He, Ya-Ling & Liu, Qing & Li, Qing, 2013. "Three-dimensional finite-difference lattice Boltzmann model and its application to inviscid compressible flows with shock waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4884-4896.
    4. Q. Li & Y. L. He & Y. Wang & G. H. Tang, 2008. "An Improved Thermal Lattice Boltzmann Model For Flows Without Viscous Heat Dissipation And Compression Work," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 125-150.
    5. Rui Du & Baochang Shi, 2009. "Incompressible Mrt Lattice Boltzmann Model With Eight Velocities In 2d Space," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1023-1037.
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    Cited by:

    1. Liu, Qing & He, Ya-Ling, 2015. "Double multiple-relaxation-time lattice Boltzmann model for solid–liquid phase change with natural convection in porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 94-106.

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