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Lattice Boltzmann method on quadtree grids.

Yu Chen1, Qinjun Kang, Qingdong Cai

  • 1The State Key Laboratory for Turbulence and Complex Systems (LTCS), Center for Applied Physics and Technology (CAPT), and Department of Mechanics and Aerospace Engineering, Peking University, Beijing, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 17, 2011
PubMed
Summary

This study introduces a lattice Boltzmann method using nonuniform quadtree grids and linear interpolation, maintaining second-order accuracy. The method efficiently simulates complex fluid dynamics problems.

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Area of Science:

  • Computational fluid dynamics
  • Numerical methods
  • Meshing techniques

Background:

  • Lattice Boltzmann methods (LBM) are powerful for fluid simulations.
  • Nonuniform grids can improve computational efficiency.
  • Quadtree grids offer adaptive meshing advantages.

Purpose of the Study:

  • To develop an accurate and efficient lattice Boltzmann method on nonuniform quadtree grids.
  • To preserve the benefits of quadtree grids in LBM simulations.
  • To maintain second-order accuracy for fluid flow problems.

Main Methods:

  • Utilized an interpolation-supplemented lattice Boltzmann model.
  • Employed linear interpolation for the streaming step on quadtree grids.
  • Integrated the back-and-forth error compensation and correction (BFECC) method.

Main Results:

  • Demonstrated preservation of quadtree grid advantages via linear interpolation.
  • Maintained second-order accuracy using the BFECC method.
  • Validated the method's accuracy and efficiency through numerical simulations.

Conclusions:

  • The proposed lattice Boltzmann method on nonuniform quadtree grids is accurate and efficient.
  • The approach effectively handles complex fluid dynamics scenarios.
  • This method offers a viable alternative for simulating fluid flows on adaptive grids.