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Hydrodynamics in Porous Media: A Finite Volume Lattice Boltzmann Study

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Abstract

Fluid flow through porous media is of great importance for many natural systems, such as transport of groundwater flow, pollution transport and mineral processing. In this paper, we propose and validate a novel finite volume formulation of the lattice Boltzmann method for porous flows, based on the Brinkman–Forchheimer equation. The porous media effect is incorporated as a force term in the lattice Boltzmann equation, which is numerically solved through a cell-centered finite volume scheme. Correction factors are introduced to improve the numerical stability. The method is tested against fully porous Poiseuille, Couette and lid-driven cavity flows. Upon comparing the results with well-documented data available in literature, a satisfactory agreement is observed. The method is then applied to simulate the flow in partially porous channels, in order to verify its potential application to fractured porous conduits, and assess the influence of the main porous media parameters, such as Darcy number, porosity and porous media thickness.

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Authors and Affiliations

  1. Honors Center of Italian Universities, H2CU, University of Rome La Sapienza, Rome, Italy

    Ahad Zarghami

  2. Science and Research Branch, Islamic Azad University, Fars, Iran

    Ahad Zarghami

  3. WARREDOC, University for Foreigners, Perugia, Italy

    Chiara Biscarini

  4. Istituto per le Applicazioni del Calcolo, CNR, Rome, Italy

    Sauro Succi

  5. DEIM, Industrial Engineering School, University of Tuscia, Viterbo, Italy

    Stefano Ubertini

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  1. Ahad Zarghami
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  2. Chiara Biscarini
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  3. Sauro Succi
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  4. Stefano Ubertini
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Correspondence to Ahad Zarghami.

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Zarghami, A., Biscarini, C., Succi, S. et al. Hydrodynamics in Porous Media: A Finite Volume Lattice Boltzmann Study. J Sci Comput 59, 80–103 (2014). https://doi.org/10.1007/s10915-013-9754-4

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