Interaction pressure tensor on high-order lattice Boltzmann models for nonideal fluids

Area of Science:

• Computational physics
• Fluid dynamics
• Statistical mechanics

Background:

• Lattice Boltzmann models (LBM) are powerful for fluid simulations.
• Incorporating nonideal interactions in LBM, especially high-order models, presents challenges.
• Pseudopotentials offer a way to model these interactions.

Purpose of the Study:

• To apply pseudopotentials directly to high-order lattice Boltzmann models.
• To derive a general expression for the pressure tensor considering nonideal interactions.
• To demonstrate thermodynamic consistency in these advanced lattice models.

Main Methods:

• Derivation of a general pressure tensor expression based on discrete lattice theory.
• Development of a generalized continuum approximation truncated at fourth-order isotropy.
• Validation against flat interface cases and the Laplace experiment.

Main Results:

• A general expression for the pressure tensor on high-order lattices was derived.
• The generalized continuum approximation is applicable to high-order lattices.
• Thermodynamic consistency was demonstrated for high-order lattice models with pseudopotentials.
• The model accurately reproduced the Laplace experiment for various lattice structures.

Conclusions:

• This work establishes a foundation for using high-order lattice models with pseudopotentials.
• The developed methods enable the simulation of nonideal fluid mixtures.
• The findings pave the way for more accurate and complex fluid dynamics simulations.