Analytic solution for a higher-order lattice Boltzmann method: slip velocity and Knudsen layer

Area of Science:

• Computational fluid dynamics
• Rarefied gas dynamics
• Numerical methods

Background:

• Lattice Boltzmann (LB) methods are widely used for fluid flow simulations.
• Standard LB methods face limitations in accurately capturing slip velocity and Knudsen layer effects at low Knudsen numbers.
• Higher-order numerical schemes are needed to improve accuracy in rarefied gas dynamics.

Purpose of the Study:

• To analyze a higher-order lattice Boltzmann method using fourth-order Gauss-Hermite quadrature.
• To investigate slip velocity and Knudsen layer phenomena in Poiseuille flows.
• To compare the performance of the higher-order LB method with the standard third-order LB method.

Main Methods:

• Developed a higher-order lattice Boltzmann method based on fourth-order Gauss-Hermite quadrature.
• Derived the exact solution for slip velocity in Poiseuille flows with finite Knudsen numbers.
• Employed a multiple relaxation time (MRT) model to analyze higher-order moment effects.

Main Results:

• The higher-order LB method provides significantly improved slip coefficients compared to the standard LB method.
• The increased accuracy in velocity space discretization enhances the prediction of slip phenomena.
• The MRT model demonstrates the influence of relaxation times on higher-order moments and slip.

Conclusions:

• The presented higher-order LB method offers superior accuracy for simulating rarefied gas flows, particularly concerning slip velocity and Knudsen layers.
• This enhanced method provides a more reliable tool for analyzing microfluidic and rarefied gas dynamics problems.
• Further investigation into MRT models can refine the understanding of complex flow behaviors in rarefied regimes.