Maxwell iteration for the lattice Boltzmann method with diffusive scaling

Area of Science:

• Fluid dynamics
• Computational physics
• Statistical mechanics

Background:

• The Navier-Stokes equations are fundamental to fluid dynamics.
• Lattice Boltzmann methods (LBM) offer a powerful computational approach.
• Existing derivations of Navier-Stokes from LBM, like Chapman-Enskog, can be complex.

Purpose of the Study:

• To present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook (BGK) models within the lattice Boltzmann method framework.
• To utilize diffusive scaling for this derivation.
• To highlight the advantages of this new method over existing ones.

Main Methods:

• Application of the Maxwell iteration technique.
• Utilizing Bhatnagar-Gross-Krook (BGK) models with diffusive scaling.
• Comparison with the Chapman-Enskog expansion method.

Main Results:

• An alternative, more straightforward derivation of the Navier-Stokes equations is achieved.
• The Maxwell iteration approach reveals important features of LBM solutions.
• The proposed method is logically clearer than traditional approaches.

Conclusions:

• The Maxwell iteration provides a simpler and more insightful path to Navier-Stokes equations from LBM.
• This derivation enhances understanding of LBM and its connection to macroscopic fluid dynamics.
• The method offers a valuable alternative for researchers in computational fluid dynamics.