Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method

Area of Science:

• Computational fluid dynamics
• Numerical methods for fluid flow
• Lattice Boltzmann methods

Background:

• Lattice Boltzmann simulations with moving boundaries often exhibit violations of Galilean invariance (GI).
• Existing methods to address this issue primarily modify momentum exchange schemes, assuming bounce-back schemes are inherently consistent with GI.
• This study challenges that assumption, identifying bounce-back schemes as the root cause of GI violations.

Purpose of the Study:

• To identify the fundamental cause of Galilean invariance violation (VGI) in lattice Boltzmann method (LBM) simulations with moving solid boundaries.
• To demonstrate that bounce-back schemes (BBS), not solely momentum exchange methods (MEM), are responsible for VGI.
• To propose and validate a novel BBS that rectifies VGI errors.

Main Methods:

• Analysis of momentum exchange and boundary forces in LBM with moving boundaries.
• Identification of VGI originating from the bounce-back scheme itself.
• Development of a coordinate transformation-based bounce-back scheme.
• Numerical simulations of laminar and turbulent flows to validate the proposed scheme.

Main Results:

• The VGI error in LBM with moving boundaries stems from the bounce-back scheme, affecting both solid and fluid phases.
• Previously proposed modified MEM schemes offer incomplete solutions to VGI.
• The proposed coordinate transformation-based BBS effectively eliminates VGI errors.
• The new scheme ensures accurate momentum exchange with minimal computational cost.

Conclusions:

• Bounce-back schemes are the primary source of Galilean invariance violations in LBM with moving boundaries.
• Modified MEM schemes alone are insufficient to fully resolve VGI.
• A coordinate transformation-based bounce-back scheme provides an effective and efficient solution for accurate simulations.