Lattice Boltzmann method with restored Galilean invariance

Area of Science:

• Computational fluid dynamics
• Lattice Boltzmann methods
• Thermodynamics

Background:

• The study builds upon existing thermal models with energy conservation, specifically referencing work by Prasianakis and Karlin (2007).
• Lattice Boltzmann methods are a powerful tool for simulating fluid dynamics, but isothermal models require careful formulation.

Purpose of the Study:

• To propose and analyze a novel isothermal model using the standard two-dimension nine-velocity lattice (D2Q9).
• To validate the model's physical properties, including invariance and isotropy.

Main Methods:

• Development of an isothermal lattice model based on a previously established thermal model.
• Simulation of shear wave and temperature wave decay using the proposed D2Q9 isothermal model and its thermal equivalent.
• Measurement of transport coefficients in a rotated moving frame of reference to assess isotropy.

Main Results:

• The proposed isothermal D2Q9 model accurately simulates wave decay phenomena.
• Both the isothermal and thermal equivalent models demonstrate Galilean invariance.
• The models exhibit reference temperature independence and rotational isotropy.

Conclusions:

• The developed isothermal D2Q9 model is a robust and physically sound tool for fluid dynamics simulations.
• The model's properties (invariance, independence, isotropy) are confirmed through rigorous testing.
• This work contributes to the advancement of isothermal lattice Boltzmann methods for scientific research.