Burnett description for plane Poiseuille flow

Area of Science:

• Fluid dynamics
• Statistical mechanics
• Computational physics

Background:

• Navier-Stokes equations fail to describe rarefied gas behavior at small Knudsen numbers.
• Previous studies using Bhatnagar-Gross-Kook models and Direct Simulation Monte Carlo (DSMC) revealed anomalous pressure and temperature profiles.
• These anomalies include bimodal temperature profiles and nonconstant pressure profiles in plane Poiseuille flow.

Purpose of the Study:

• Compare Direct Simulation Monte Carlo (DSMC) measurements with numerical solutions of the Burnett equations for plane Poiseuille flow.
• Evaluate the suitability of Burnett equations for describing non-equilibrium phenomena in rarefied gases at larger Knudsen numbers.
• Investigate the ability of Burnett equations to reproduce anomalous hydrodynamic behaviors observed in previous studies.

Main Methods:

• Numerical solutions of the Burnett equations.
• Comparison with Direct Simulation Monte Carlo (DSMC) experimental data.
• Analysis of hydrodynamic variables and non-equilibrium fluxes.

Main Results:

• Burnett equations do not predict the bimodal temperature profile observed in DSMC.
• Burnett equations successfully reproduce other anomalous features, such as nonconstant pressure and nonzero parallel heat flux.
• The Burnett equations show better agreement with molecular-dynamics simulations for shock waves compared to Navier-Stokes.

Conclusions:

• Burnett equations offer an improved description over Navier-Stokes for rarefied gas dynamics at larger Knudsen numbers.
• While not fully capturing all anomalies, Burnett equations reproduce key non-equilibrium features in Poiseuille flow.
• Further investigation into higher-order kinetic models may be necessary to fully capture bimodal temperature profiles.