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Implicit discretization and nonuniform mesh refinement approaches for FD discretizations of LBGK Models

Author

Listed:
  • Jonas Tölke

    (Lst. Bauinformatik, Techn. Univ. München, Arcisstr. 21, D-80290, Germany)

  • Manfred Krafczyk

    (Lst. Bauinformatik, Techn. Univ. München, Arcisstr. 21, D-80290, Germany)

  • Manuel Schulz

    (Lst. Bauinformatik, Techn. Univ. München, Arcisstr. 21, D-80290, Germany)

  • Ernst Rank

    (Lst. Bauinformatik, Techn. Univ. München, Arcisstr. 21, D-80290, Germany)

  • Rodolfo Berrios

    (Esc. Ing. Mec., Universidad Central de Venezuela, Caracas, Los Chaguaramos, Caracas, Venezuela)

Abstract

After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.

Suggested Citation

  • Jonas Tölke & Manfred Krafczyk & Manuel Schulz & Ernst Rank & Rodolfo Berrios, 1998. "Implicit discretization and nonuniform mesh refinement approaches for FD discretizations of LBGK Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1143-1157.
    • Handle: RePEc:wsi:ijmpcx:v:09:y:1998:i:08:n:s0129183198001059
    DOI: 10.1142/S0129183198001059
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