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Multireflection boundary conditions for lattice Boltzmann models.

Irina Ginzburg1, Dominique d'Humières

  • 1Fraunhofer Institut für Techno und Wirtschaftsmathematik, Gottlieb-Daimler-Strasse 49, Kaiserslautern D-67663, Germany. irina.ginzburg@cemagref.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 3, 2004
PubMed
Summary

New boundary conditions for lattice Boltzmann models significantly improve accuracy for fluid flow simulations. These multireflection conditions offer smoother fields and near-analytical results, even at low resolutions.

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Statistical physics

Background:

  • Lattice Boltzmann models (LBM) are widely used for simulating fluid dynamics.
  • Existing boundary conditions in LBM, like bounce-back, have limitations in accuracy.
  • Third-order kinetic accuracy is desired for general flow simulations.

Purpose of the Study:

  • To develop a general framework for analyzing existing LBM boundary conditions.
  • To design novel, third-order kinetic accurate boundary conditions for LBM.
  • To enhance the accuracy and stability of LBM simulations for complex flows.

Main Methods:

  • Developed a theoretical framework for link-type boundary conditions in LBM.
  • Introduced new multireflection boundary conditions.

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  • Performed numerical simulations for Stokes and Navier-Stokes flows, including flows in periodic arrays of spheres and cylinders.

    • Main Results:

    • New boundary conditions enable exact solutions for Couette and Poiseuille flows in the Stokes limit.
    • Linear interpolations show up to an order of magnitude improvement in accuracy over bounce-back.
    • Multireflection boundary conditions achieve accuracy close to quasi-analytical solutions with improved field smoothness and stability.

    Conclusions:

    • The proposed framework provides tools for studying and improving LBM boundary conditions.
    • Novel multireflection boundary conditions offer significant accuracy and stability enhancements for LBM simulations.
    • These advancements are crucial for accurate simulations of fluid dynamics, especially near complex geometries.