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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Onsager-regularized lattice Boltzmann method: A nonequilibrium thermodynamics-based regularized lattice Boltzmann

Anirudh Jonnalagadda¹, Atul Sharma¹, Amit Agrawal¹

¹Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai-400076, India.

Physical Review. E

|August 20, 2021

Summary

This study introduces a novel kinetic theory approach for lattice Boltzmann methods (LBMs), enhancing simulation stability and accuracy. The new method improves upon existing regularized LBM schemes for complex fluid dynamics problems.

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Area of Science:

Computational fluid dynamics
Kinetic theory
Thermodynamics

Background:

Regularized lattice Boltzmann methods (LBMs) improve upon the standard Bhatnagar-Gross-Krook method by filtering nonhydrodynamic moments.
Existing methods often use multiscale or Hermite polynomial expansions for evaluating regularized populations.

Purpose of the Study:

To propose an alternative approach for evaluating lattice populations in LBMs.
To develop a method based on kinetic theory consistent with nonequilibrium thermodynamics and the Onsager-reciprocity principle.

Main Methods:

A novel kinetic theory approach for evaluating lattice populations.
Verification and validation across canonical fluid dynamics problems including shock tubes, shear layers, lid-driven cavities, flow past cylinders, and Poiseuille flow.
Comparison with existing regularized LBM schemes.

Main Results:

The proposed method demonstrates significant improvements in simulation stability.
Enhanced accuracy was observed in simulations compared to existing regularized LBM schemes.
Successful validation across a range of non-vanishing Knudsen number flows.

Conclusions:

The new kinetic theory-based LBM approach offers superior stability and accuracy.
This method provides a robust alternative for simulating complex fluid dynamics problems.
The findings contribute to advancing the capabilities of LBM for scientific research.