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Lattices for the lattice Boltzmann method.

Shyam S Chikatamarla1, Iliya V Karlin

  • 1LAV, Institute of Energy Technology, ETH Zurich, 8092 Zurich, Switzerland. shyam_css@yahoo.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

This study details higher-order lattice Boltzmann models, presenting a general construction theory and discovering new, accurate, and stable lattices for fluid dynamics simulations.

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Area of Science:

  • Computational fluid dynamics
  • Mathematical physics

Background:

  • The Boltzmann equation is a fundamental kinetic theory model for describing fluid behavior.
  • Lattice Boltzmann models offer a computationally efficient approximation to the Boltzmann equation.
  • Higher-order models aim to improve the accuracy of lattice Boltzmann methods.

Purpose of the Study:

  • To elaborate on the recently introduced theory of higher-order lattice Boltzmann models.
  • To present a general theory for constructing lattice Boltzmann models as approximations to the Boltzmann equation.
  • To identify and classify new lattice structures based on their accuracy and stability.

Main Methods:

  • Development of a general theoretical framework for constructing lattice Boltzmann models.
  • Classification of newly discovered lattices based on their approximation degree to the Boltzmann equation.
  • Analysis of numerical stability using the entropy principle.
  • Demonstration of lattice efficiency and accuracy through multidimensional simulations.

Main Results:

  • A detailed elaboration of higher-order lattice Boltzmann model theory.
  • Discovery of new lattice structures in all three spatial dimensions.
  • Classification of these lattices according to their accuracy in approximating the Boltzmann equation.
  • Validation of numerical stability through entropy-based arguments.
  • Empirical demonstration of the efficiency and accuracy of numerous new lattices.

Conclusions:

  • The presented general theory provides a systematic approach to constructing accurate lattice Boltzmann models.
  • Newly discovered lattices offer improved approximations to the Boltzmann equation with demonstrated numerical stability.
  • These findings advance the field of computational fluid dynamics by providing more efficient and accurate simulation tools.