Galilean-invariant lattice-Boltzmann models with H theorem

Area of Science:

• Computational fluid dynamics
• Statistical mechanics
• Numerical analysis

Background:

• Entropic lattice-Boltzmann models are crucial for simulating fluid dynamics.
• Galilean invariance is a fundamental physical principle that must be preserved in fluid models.
• Existing models may face limitations in stability or applicability across different dimensions.

Purpose of the Study:

• To determine the specific H function required by Galilean invariance in entropic lattice-Boltzmann models.
• To construct a novel lattice-Boltzmann model that is fully explicit, unconditionally stable, and Galilean-invariant.
• To analyze the performance limitations of the proposed model, particularly concerning attainable Reynolds numbers.

Main Methods:

• Derivation of the H function based on the principle of Galilean invariance.
• Construction of a lattice-Boltzmann model incorporating the derived H function.
• Analysis of the model's stability and performance characteristics, including Reynolds number limitations.

Main Results:

• The H function is identified as Burg entropy for D=2 and Tsallis entropy (q=1-(2/D)) for D>2.
• A fully explicit, unconditionally stable, Galilean-invariant lattice-Boltzmann model for incompressible Navier-Stokes equations was successfully constructed.
• The model's attainable Reynolds number is demonstrated to be limited solely by grid resolution.

Conclusions:

• Galilean invariance provides a powerful constraint for selecting H functions in entropic lattice-Boltzmann models.
• The developed model offers significant advantages in terms of stability and explicit formulation.
• This work advances the development of accurate and efficient computational fluid dynamics tools.