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Lattice Boltzmann method on quadtree grids for simulating fluid flow through porous media: A new automatic algorithm

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  • Foroughi, Sajjad
  • Jamshidi, Saeid
  • Masihi, Mohsen

Abstract

During the past two decades, the lattice Boltzmann (LB) method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations. In this method, instead of solving the Navier Stocks equation, the Boltzmann equation is solved to simulate the flow of a fluid. This method was originally developed based on uniform grids. However, in order to model complex geometries such as porous media, it can be very slow in comparison with other techniques such as finite differences and finite elements. To eliminate this limitation, a number of studies have aimed to formulate the lattice Boltzmann on the unstructured grids. This paper deals with simulating fluid flow through a synthetic porous medium using the LB method and on the quadtree grid structure. To this end, the LB method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media. Accuracy and efficiency of this algorithm is compared against the conventional LB method based on uniform grids. While the decrease in computational time in the proposed LB method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images, the same level of accuracy is obtained when compared with the conventional LB method on uniform grids.

Suggested Citation

  • Foroughi, Sajjad & Jamshidi, Saeid & Masihi, Mohsen, 2013. "Lattice Boltzmann method on quadtree grids for simulating fluid flow through porous media: A new automatic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4772-4786.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:20:p:4772-4786
    DOI: 10.1016/j.physa.2013.05.047
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    References listed on IDEAS

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    1. Yu, Dazhi & Girimaji, Sharath S., 2006. "Multi-block Lattice Boltzmann method: Extension to 3D and validation in turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(1), pages 118-124.
    2. Chen, H. & Filippova, O. & Hoch, J. & Molvig, K. & Shock, R. & Teixeira, C. & Zhang, R., 2006. "Grid refinement in lattice Boltzmann methods based on volumetric formulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(1), pages 158-167.
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    Cited by:

    1. Lee, Hyun Geun & Kim, Junseok, 2015. "An efficient numerical method for simulating multiphase flows using a diffuse interface model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 423(C), pages 33-50.
    2. Zhang, Xiaoying & Ma, Funing & Yin, Shangxian & Wallace, Corey D & Soltanian, Mohamad Reza & Dai, Zhenxue & Ritzi, Robert W. & Ma, Ziqi & Zhan, Chuanjun & Lü, Xiaoshu, 2021. "Application of upscaling methods for fluid flow and mass transport in multi-scale heterogeneous media: A critical review," Applied Energy, Elsevier, vol. 303(C).

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