Skip to main content
SpringerLink
Log in

Microcosmic bound theorem of Daycy’s law and its application

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

By combining Chapman-Enskog expansion with the BGK approximation to Baltzmann equation and Navier-Stokes equation was obtained. And an expression of Darcy’s law was obtained through taking variable average over Navier-Stokes equation on some representative space in porous media, and finally an example was taken to prove its reliability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. XU You-sheng, LIU Ci-qun, YU Hui-dan. New studying of lattice Boltzmann methods for two-phase driven in porous mdeia[J].Applied Mathematics and Mechanics (English Edition), 2002,23(4):387–392.

    Google Scholar 

  2. Spaid M A A, Phelan F R. Lattice Boltzmann methods for modeling microscale flow in fibrous porous media[J].Physics of Fluids, 1997,9(9):2468–2474.

    Article  MathSciNet  Google Scholar 

  3. Cercignani C.The Boltzmann Equation and Its Applications[M]. New York: Springer, 1988.

    Google Scholar 

  4. Irmay S. On the hydraulic conductivity of unsaturated soils[J].Trans Amer Geophys, 1954, (35): 463–468.

  5. Frisch U. Relation between the lattice Boltzmann equation and the Navier-Stokes equations[J].Physica D, 1991,47(7):231–232.

    Article  Google Scholar 

  6. Bhatnagar P, Gross E P, Krook M K. A model for collision processes in gases—I: Small amplitude processes in charged and neutral one-component systems[J].Physics Reviews, 1954,94(3): 515–525.

    Google Scholar 

  7. Bear J.Dymanics of Fluids in Porous Media[M]. New York: American Elsevier Publishing Company. 1972,111.

    Google Scholar 

  8. Polubarinova-Kochina P Y. Unsteady seepage with an interface[J].Nauk SSSR, 1949, (66): 173–176. (in Russian)

  9. CHEN Shi-yi, WANG Zhi, SHAN Xiao-wen,et al. Lattice Boltzmann computationl fluid dynamics in three dimensions [J].Stat Phys, 1992,68(3/4):379–400.

    Google Scholar 

  10. Cornubert R, d’Hunières D, Levermore D. A knudsen layer theory for lattice gases[J].Physica D, 1991,47(1):241–259.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institude of Mathematics & Physics & Information Science, Zhejiang Normal University, 321004, Jinhua, Zhejiang, P. R. China

    Xu You-sheng & Lin Ji

  2. Institude of Porous Flow and Fluid Mechanics, Academia Sinica, 065007, Langfang, Hebei, P. R. China

    Liu Ci-qun

Authors
  1. Xu You-sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liu Ci-qun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lin Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Liu Ci-qun, Original Member of Editorial Committee, AMM

Foundation items: the National Natural Science Foundation of China (10372094); the Natural Science Foundation of Zhejiang Province, China (M103082, M102053); the Science Foundation of Education Department of Zhejiang Province, China (20030871)

Biography: Xu You-sheng (1963∼), Associate Professor, Doctor

Rights and permissions

Reprints and permissions

About this article

Cite this article

You-sheng, X., Ci-qun, L. & Ji, L. Microcosmic bound theorem of Daycy’s law and its application. Appl Math Mech 25, 279–287 (2004). https://doi.org/10.1007/BF02437331

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02437331

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation