Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient...

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis
• Fluid Mechanics

Background:

• Standard Lattice Boltzmann (LB) models for Navier-Stokes (NS) equations can produce non-Galilean-invariant (GI) viscous stress with cubic velocity errors.
• Existing methods to restore GI often involve modified collision operators, affecting relaxation times or moment equilibria.

Purpose of the Study:

• To present a GI formulation of the preconditioned cascaded central-moment LB method for steady flows.
• To eliminate cubic velocity errors in the preconditioned NS equations solved by the LB method on standard lattices.
• To validate the method's effectiveness in convergence acceleration and accuracy improvement.

Main Methods:

• Developed a GI formulation for the preconditioned cascaded central-moment LB method.
• Employed Chapman-Enskog analysis to identify and analyze spurious non-GI defect terms.
• Introduced corrections to cubic velocity terms and extended moment equilibria, dependent on the preconditioning parameter.

Main Results:

• The proposed method is free of cubic velocity errors on a standard lattice for steady flows.
• Anisotropy of viscous stress depends on the preconditioning parameter and fluid velocity.
• Corrections based on scaling and extended moment equilibria fully restore Galilean invariance without cubic defects.

Conclusions:

• The preconditioning parameter significantly influences non-GI errors and their corrections.
• The GI preconditioned central-moment LB method effectively accelerates convergence and enhances accuracy.
• Validated the method on complex flow benchmark problems, demonstrating its robustness and efficacy.