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Lattice Boltzmann model for the convection-diffusion equation.

Zhenhua Chai1, T S Zhao

  • 1Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon Hong Kong SAR, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 16, 2013
PubMed
Summary

We developed a new lattice Boltzmann (LB) model for the convection-diffusion equation (CDE). This model offers local computation for heat and mass transfer in complex geometries, improving accuracy and efficiency.

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Area of Science:

  • Computational fluid dynamics
  • Numerical methods for partial differential equations
  • Heat and mass transfer

Background:

  • The convection-diffusion equation (CDE) is fundamental in modeling transport phenomena.
  • Traditional numerical methods for CDE can be computationally intensive, especially in complex geometries.
  • Existing lattice Boltzmann (LB) models for CDE often involve nonlocal computations, limiting their efficiency.

Purpose of the Study:

  • To propose a novel lattice Boltzmann (LB) model for the convection-diffusion equation (CDE).
  • To enable local computation of collision processes for enhanced efficiency in complex geometries.
  • To develop and validate a local scheme for heat and mass flux computation with improved accuracy.

Main Methods:

  • Development of a new lattice Boltzmann (LB) model for the convection-diffusion equation (CDE).
  • Application of Chapman-Enskog analysis to recover the CDE from the LB model.
  • Implementation of a local scheme for computing heat and mass fluxes, replacing nonlocal finite-difference schemes.
  • Validation against analytical solutions for classical problems to assess convergence and accuracy.

Main Results:

  • The proposed LB model correctly recovers the convection-diffusion equation (CDE) via Chapman-Enskog analysis.
  • The model enables local collision processes, suitable for heat and mass transfer in complex geometries.
  • The local flux computation scheme achieves second-order spatial convergence.
  • The new LB model demonstrates higher accuracy compared to existing LB models for the CDE.

Conclusions:

  • The developed LB model provides an accurate and efficient method for solving the CDE.
  • The local computation scheme significantly enhances the applicability of LB methods for heat and mass transfer in complex domains.
  • This approach offers a superior alternative to existing LB models for CDE simulations.