Immersed boundary lattice Boltzmann model based on multiple relaxation times

Area of Science:

• Computational fluid dynamics
• Numerical methods

Background:

• The immersed boundary lattice Boltzmann method (IB-LBM) is a powerful tool for simulating fluid-structure interactions.
• Current IB-LBM versions, particularly those using single relaxation time (SRT), suffer from significant numerical boundary slip.
• This slip can compromise the accuracy of simulations.

Purpose of the Study:

• To develop an improved immersed boundary lattice Boltzmann model that minimizes numerical boundary slip.
• To introduce a multiple relaxation time (MRT) approach within the IB-LBM framework.
• To provide a more accurate and stable numerical method for fluid dynamics simulations.

Main Methods:

• Proposed a novel immersed boundary lattice Boltzmann model utilizing multiple relaxation times (MRT).
• Introduced a specific relationship between relaxation time parameters within the MRT-IB-LBM.
• Conducted rigorous mathematical analysis and numerical experiments to validate the model.

Main Results:

• The proposed MRT-IB-LBM dramatically reduces numerical boundary slip compared to SRT-based models.
• A special formula for relaxation time parameters was derived and applied.
• Numerical experiments confirmed the significant improvement in accuracy and reduction of slip.

Conclusions:

• The MRT-IB-LBM effectively mitigates numerical boundary slip, a common issue in SRT-IB-LBM.
• This new model offers enhanced accuracy for simulations involving complex boundaries.
• The findings pave the way for more reliable computational fluid dynamics simulations.