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A study on the inclusion of body forces in the lattice Boltzmann BGK equation to recover steady-state hydrodynamics

Author

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  • Silva, Goncalo
  • Semiao, Viriato

Abstract

When the lattice Boltzmann (LB) method is used to solve hydrodynamic problems containing a body force term varying in space and/or time, its modelling at the mesoscopic scale must be verified in terms of consistency in order to avoid the appearance of non-hydrodynamic error terms at the macroscopic scale. In the present work it is shown that the modelling of spatially varying steady body force terms in the LB equation must be different from the time-dependent case, when a steady-state flow solution is sought. For that, the Chapman–Enskog analysis is used to derive the LB body force model for the LB BGK equations in a steady-state flow problem. The theoretical findings are supported by numerical tests performed on two different 2D steady-state laminar flows driven by spatially varying body forces with known analytical solutions.

Suggested Citation

  • Silva, Goncalo & Semiao, Viriato, 2011. "A study on the inclusion of body forces in the lattice Boltzmann BGK equation to recover steady-state hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1085-1095.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:6:p:1085-1095
    DOI: 10.1016/j.physa.2010.11.037
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    Citations

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    Cited by:

    1. Farnoush, Somayeh & Manzari, Mehrdad T., 2014. "An investigation on the body force modeling in a lattice Boltzmann BGK simulation of generalized Newtonian fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 315-332.
    2. Krivovichev, Gerasim V., 2019. "Stability analysis of body force action models used in the single-relaxation-time single-phase lattice Boltzmann method," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 25-41.
    3. Mapelli, Vinícius Pessoa & Czelusniak, Luiz Eduardo & Guzella, Matheus dos Santos & Cabezas-Gómez, Luben, 2022. "On the force scheme influence on pseudopotential method coexistence curve," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).

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