Enhanced multi-relaxation-time lattice Boltzmann model by entropic stabilizers

Area of Science:

• Computational fluid dynamics
• Numerical methods in physics
• Statistical mechanics

Background:

• The multi-relaxation-time lattice Boltzmann model (MRT-LBM) is a powerful numerical method for simulating fluid dynamics.
• A key challenge in MRT-LBM is the selection of appropriate relaxation rates, which significantly impacts simulation stability and accuracy.
• Existing methods often rely on constant relaxation rates, limiting the model's adaptability to complex flow phenomena.

Purpose of the Study:

• To develop an enhanced MRT-LBM that overcomes the difficulty of choosing relaxation rates.
• To introduce a method where relaxation rates evolve dynamically with time.
• To demonstrate the efficacy of the enhanced MRT-LBM across various benchmark fluid flow problems.

Main Methods:

• The study proposes solving a least-square problem for entropic stabilizer equations to determine relaxation rates.
• Nonequilibrium populations are decomposed into modes using the inverse transform matrix to derive these entropic stabilizer equations.
• The H-function is minimized to achieve the entropic stabilizer equations, ensuring numerical stability.
• Different moment representations (Gram-Schmidt orthogonal, natural, central) are investigated.

Main Results:

• The enhanced MRT-LBM successfully implements time-evolving relaxation rates, addressing the challenge of fixed rate selection.
• The method was tested on double periodic shear flow, shock tube problems, and lid-driven cavity flow.
• The simulations demonstrated the robustness and potential of the enhanced MRT-LBM.

Conclusions:

• The proposed method effectively surmounts the challenge of selecting relaxation rates in MRT-LBM.
• The enhanced MRT-LBM with dynamic relaxation rates shows significant potential for accurate and stable fluid dynamics simulations.
• This advancement offers a more flexible and adaptive approach to lattice Boltzmann modeling.