Closure equation and higher-order moment relations in the Gauss-Hermite lattice Boltzmann method

Area of Science:

• Computational Fluid Dynamics
• Mathematical Physics
• Numerical Analysis

Background:

• Moment methods are crucial for solving transport problems governed by the Boltzmann-BGK equation.
• These methods necessitate closure equations to relate higher-order moments to lower-order ones due to underdetermined moment equations.

Purpose of the Study:

• To investigate the closure equation and higher-order moment relations within the lattice Boltzmann method (LBM) when using Gauss-Hermite quadrature for discrete velocity sets.
• To provide a general formula for efficient computation of higher-order moments in LBM.

Main Methods:

• Analysis of closure relations implicit in LBM with Gauss-Hermite quadrature discrete velocity sets.
• Derivation of a general formula for evaluating higher-order moments.
• Validation of derived formulas using numerical implementations of LBM for steady Couette flow.

Main Results:

• The discrete velocity set in LBM intrinsically defines the closure equation and higher-order moment relations.
• A general formula was developed for efficient computational evaluation of higher-order moments.
• Derived formulas were validated against numerical simulations of steady Couette flow.

Conclusions:

• The inherent closure properties of LBM discrete velocity sets are elucidated.
• The developed general formula offers computational efficiency and theoretical insight into LBM.
• The findings are expected to benefit theoretical analyses of LBM performance in transport phenomena.