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Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.

Zhaoli Guo1, T S Zhao

  • 1Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Hong Kong, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
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A new explicit finite-difference lattice Boltzmann method using curvilinear coordinates enhances computational efficiency and numerical stability. This method improves upon implicit schemes for fluid dynamics simulations, offering better performance.

Area of Science:

  • Computational Fluid Dynamics
  • Numerical Analysis
  • Fluid Mechanics

Background:

  • Existing lattice Boltzmann methods (LBM) with implicit collision terms can suffer from computational inefficiency and numerical instability.
  • Previous work by Mei and Shyy (1998) utilized implicit treatment for the Bhatnagar-Gross-Krook (BGK) collision term.

Purpose of the Study:

  • To develop an explicit finite-difference lattice Boltzmann method for curvilinear coordinates.
  • To enhance the computational efficiency and numerical stability of existing LBM.

Main Methods:

  • A novel distribution function was introduced to remove the implicitness of the numerical scheme.
  • The finite-difference approach was adapted for curvilinear coordinates within the lattice Boltzmann framework.
  • The explicit scheme was applied to various benchmark fluid flow problems.

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Main Results:

  • The proposed explicit finite-difference LBM in curvilinear coordinates demonstrated improved computational efficiency and numerical stability.
  • Numerical simulations for 2D Poiseuille flow, unsteady Couette flow, lid-driven cavity flow, and flow past a circular cylinder yielded results consistent with prior studies.
  • The method proved effective for complex geometries and flow conditions.

Conclusions:

  • The developed explicit finite-difference lattice Boltzmann method offers a more efficient and stable alternative for fluid flow simulations in curvilinear coordinates.
  • The approach shows promise for extension to other LBM models and non-uniform meshes.
  • This work contributes to advancing numerical techniques in computational fluid dynamics.