Stabilization of the lattice Boltzmann method using the Ehrenfests' coarse-graining idea

Area of Science:

• Computational Fluid Dynamics
• Numerical Methods
• Statistical Mechanics

Background:

• The lattice Boltzmann method (LBM) is a popular numerical technique for simulating complex fluid dynamics due to its computational efficiency.
• A significant limitation of LBM is its susceptibility to numerical instabilities, particularly near shock waves.

Purpose of the Study:

• To develop a simple and effective method for stabilizing the lattice Boltzmann method.
• To address the issue of numerical instabilities in LBM simulations, especially in challenging flow regimes.

Main Methods:

• A novel stabilization technique, termed Ehrenfests' steps, is proposed.
• This method involves monitoring the difference between microscopic and macroscopic entropy.
• Populations are reset to equilibrium states when a predefined entropy difference threshold is exceeded, drawing inspiration from Ehrenfests' coarse-graining concept.

Main Results:

• The proposed Ehrenfests' steps effectively stabilize the lattice Boltzmann method.
• The technique addresses numerical instabilities without compromising the method's efficiency for complex fluid flow modeling.

Conclusions:

• Ehrenfests' steps offer a straightforward yet powerful solution for enhancing the robustness of LBM.
• This stabilization technique improves the reliability of LBM for simulating complex fluid flows, including those with shock phenomena.