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Filter-matrix lattice Boltzmann model for microchannel gas flows.

Congshan Zhuo1, Chengwen Zhong1

  • 1National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

The filter-matrix lattice Boltzmann (FMLB) model accurately simulates microchannel gas flows across slip and transition regimes. A revised kinetic boundary condition improves predictions for higher Knudsen numbers.

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Area of Science:

  • Computational fluid dynamics
  • Microfluidics
  • Rarefied gas dynamics

Background:

  • The lattice Boltzmann method (LBM) is effective for microscale gas flows.
  • Research interest in microscale gas flows is significant.
  • The filter-matrix lattice Boltzmann (FMLB) model is a recent advancement.

Purpose of the Study:

  • Apply the FMLB model to microchannel gas flows.
  • Investigate flow behaviors in the transition regime using effective viscosity.
  • Develop and validate a kinetic boundary condition for the FMLB model.

Main Methods:

  • Utilized a Bosanquet-type effective viscosity for the transition regime.
  • Designed a combined bounce-back and specular-reflection scheme with a second-order slip scheme.
  • Derived slip velocity and discrete effects within the FMLB model.
  • Introduced a fitting function with slip coefficients for a revised second-order slip boundary condition.

Main Results:

  • Validated the revised scheme through numerical simulations.
  • Achieved accurate simulations across a wide range of Knudsen numbers (slip and transition regimes).
  • Numerical results for velocity profiles, mass flow rates, and pressure distribution showed good agreement with established methods (linearized Boltzmann equation, DSMC, experimental data).

Conclusions:

  • The FMLB model with the revised kinetic boundary condition provides accurate simulations for microchannel gas flows.
  • The model demonstrates improved predictions for higher Knudsen numbers in the transition regime.
  • The study validates the effectiveness of the FMLB model and the developed boundary condition for microscale gas flow analysis.