Discrete lattice effects on the forcing term in the lattice Boltzmann method

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Statistical mechanics

Background:

• The lattice Boltzmann equation (LBE) is a powerful numerical method for simulating fluid flow.
• Accurate incorporation of forcing terms in LBE is essential for modeling complex fluid phenomena.
• Existing methods for handling forces in LBE may not fully account for discrete lattice effects.

Purpose of the Study:

• To demonstrate the necessity of considering discrete lattice effects when implementing forcing terms in the LBE.
• To propose a novel representation for the forcing term in the LBE.
• To derive the Navier-Stokes equation from the LBE using the proposed forcing term representation and analyze its validity.

Main Methods:

• Chapman-Enskog expansion applied to the lattice Boltzmann equation.
• Development and implementation of a new forcing term representation.
• Comparative analysis of the proposed method with existing force treatments in LBE.

Main Results:

• Discrete lattice effects significantly influence the introduction of forces into the LBE.
• The proposed forcing term representation enables the derivation of the Navier-Stokes equation from the LBE.
• The new representation offers a more rigorous approach compared to some existing methods.

Conclusions:

• Accounting for discrete lattice effects is fundamental for accurate force implementation in LBE.
• The proposed forcing term representation provides a valid and improved method for LBE simulations.
• This work contributes to the theoretical foundation and practical application of the lattice Boltzmann method in fluid dynamics.