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Grid Technologies in Lattice Boltzmann Method: A Comprehensive Review

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  • Bo An

    (School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
    National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Xi’an 710072, China
    The Youth Innovation Team of Shaanxi Universities, Team of Numerical Algorithm Innovation, Xi’an 710072, China)

  • K. D. Chen

    (School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China)

  • J. M. Bergadà

    (Fluid Mechanics Department, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain)

Abstract

A review of the development of grid technologies and corresponding numerical approaches based on the lattice Boltzmann method (LBM) is performed in the present study. The history of the algorithmic development and practical applications is presented and followed by a short introduction of the basic theory of LBM, especially the classic lattice Bhatnagar–Gross–Krook LBGK D2Q9 model. In reality, all the different grid technologies reported aim to solve one but very important problem, the local grid refinement, which largely influences the stability, efficiency, accuracy, and flexibility of the conventional LBM. The improvement of these numerical properties after employing various grid technologies is analyzed. Several grid technologies, such as body-fitted grid, multigrid, non-uniform rectangular grid, quadtree Cartesian square grid, unstructured grid and meshless discrete points, as well as the corresponding numerical approaches are compared and discussed.

Suggested Citation

  • Bo An & K. D. Chen & J. M. Bergadà, 2025. "Grid Technologies in Lattice Boltzmann Method: A Comprehensive Review," Mathematics, MDPI, vol. 13(17), pages 1-29, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2861-:d:1742345
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