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Updated: Jul 6, 2026

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

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Published on: December 4, 2017

Lattice Boltzmann equation linear stability analysis: thermal and athermal models.

D N Siebert¹, L A Hegele, P C Philippi

¹LMPT Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianopolis, SC, Brazil. diogo@lmpt.ufsc.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 21, 2008

Summary

This study analyzes lattice Boltzmann models for nonisothermal compressible flows. Higher-order approximations improve stability, offering better solutions for complex fluid dynamics simulations.

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Area of Science:

Computational Fluid Dynamics
Thermodynamics
Numerical Analysis

Background:

Lattice Boltzmann models (LBM) struggle with nonisothermal compressible flows due to deviations from macroscopic equations and numerical instabilities.
Existing thermal LBMs require further development for accurate and stable simulations of such flows.

Purpose of the Study:

Investigate sources of instability in recently derived LBMs for nonisothermal compressible flows.
Determine stability limits for macroscopic variables in these LBMs.
Enhance the stability and accuracy of LBM for complex thermal fluid simulations.

Main Methods:

Linear stability analysis of LBMs derived from the continuous Boltzmann equation.
Evaluation of two-dimensional (2D) lattices with varying velocities (9, 17, 25, 37).
Incorporation of third-order terms into an athermal 2D nine-velocity model to improve accuracy.

Main Results:

Increasing the order of approximation in LBMs enhances numerical stability.
Specific stability limits for macroscopic variables were identified for different lattice configurations.
The modified athermal 2D nine-velocity model shows improved accuracy over the standard D2Q9 model.

Conclusions:

Higher-order lattice Boltzmann approximations are crucial for stable nonisothermal compressible flow simulations.
The identified stability limits provide practical guidelines for model selection and parameterization.
Further development of LBMs, including the incorporation of higher-order terms, is essential for advancing computational fluid dynamics in thermal applications.