Self-consistent force scheme in the spectral multiple-relaxation-time lattice Boltzmann model.

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis
• Statistical Mechanics

Background:

• The Lattice Boltzmann Method (LBM) is a powerful numerical technique for fluid dynamics.
• Accurate incorporation of force terms is crucial for LBM simulations, especially for complex flows.
• Existing methods for force terms in high-order LBM can lack self-consistency.

Purpose of the Study:

• To derive a novel force term for the spectral multiple-relaxation-time high-order lattice Boltzmann model.
• To ensure the self-consistency of the force term in both isothermal and thermal flow simulations.
• To provide a framework for practical numerical implementation of the derived force term.

Main Methods:

• Expansion of the Boltzmann equation's force term in the Hermite temperature rescaled central moment (RCM) space.
• Neglecting higher-order nonequilibrium RCM moments.
• Incorporation of the force term within the RCM collision operator.
• Transformation between RCM and raw moment (RM) spaces for numerical implementation.

Main Results:

• A new force term scheme is derived for the spectral MRT high-order LBM.
• The derived force term is demonstrated to be self-consistent for isothermal flows.
• The scheme is also shown to be self-consistent for compressible thermal flows with adjustable Prandtl numbers.
• Numerical experiments validate the self-consistency and applicability of the new force term.

Conclusions:

• The developed force term scheme is a significant advancement for high-order LBM.
• The method offers improved accuracy and reliability for simulating isothermal and thermal fluid flows.
• This work provides a robust approach for incorporating force terms in advanced LBM.