[论文解读] Small Rarefaction, Large Consequences: Limits of Navier Stokes Turbulence Simulations

Songyan Tian, Lei Wu|arXiv (Cornell University)|Feb 9, 2026

Gas Dynamics and Kinetic Theory被引用 0

一句话总结

该论文表明，在湍流射流冲击中，弱稀薄效应在局部可以占主导地位，导致对纳维-斯托克斯方程预测的表面剪应力和热流量产生显著误差，这一点通过直接 Boltzmann 模拟揭示。

ABSTRACT

We conduct numerical simulations of rocket plume impingement on a lunar landing surface using two complementary frameworks: the Boltzmann equation, which naturally captures rarefied gas dynamics, and the Navier Stokes (NS) equations, the conventional workhorse for turbulent flow simulations. We show that subtle rarefaction effects, long considered negligible in turbulent regimes, can become locally dominant within shear layers where viscous stresses predicted by the NS constitutive relation undergo sign reversals. This phenomenon, which we term constitutive degeneracy, produces order-one relative errors in predicted surface shear stress and heat flux. Our results demonstrate that turbulence can expose hidden limits of NS equations with broad implications for high-speed aerodynamics and planetary exploration.

研究动机与目标

• Motivate investigation of rarefaction effects in turbulent, inhomogeneous flows relevant to aerospace scenarios.
• Assess limits of Navier–Stokes turbulence modeling in the presence of localized rarefaction.
• Demonstrate constitutive degeneracy where non-equilibrium stresses govern surface loads.
• Compare continuum(NS) predictions with kinetic(Boltzmann) solutions in a jet-impingement setup.
• Provide insights for high-speed aerodynamics and planetary exploration applications.

提出的方法

• Solve Boltzmann equation using a discrete velocity method with a modified Rykov collision model for nitrogen exhaust.
• Couple a coarse-grained GSIS–SST framework to capture multiscale continuum-rarefied dynamics without explicit domain decomposition.
• Perform time-resolved Boltzmann simulations to verify turbulence and rarefaction interactions beyond SST closure.
• Analyze constitutive relations by decomposing total stress into NS (laminar+SST) and Boltzmann non-equilibrium components.
• Evaluate local Knudsen numbers and gradient-length Kn to identify degenerate regions where NS stress vanishes or reverses sign.
• Use direct numerical Boltzmann results to contrast against NS-SST predictions in key regions.

Figure 1: (a) The density gradient and streamlines. (b) Shear stress at the ground surface. (c) The turbulent-to-laminar viscosity ratio $\mu_{r}$ and the local Knudsen number $\text{Kn}_{gll}$ , in the left and right half-domains, respectively. (d) Heat flux at the ground surface. (e) Contour of th

实验结果

研究问题

• RQ1 Do weak rarefaction effects influence macroscopic turbulent loads in localized shear layers?
• RQ2 Does the NS constitutive relation degenerate in regions of flow turning or recirculation, leading to large errors in surface stress and heat flux?
• RQ3 How do higher-order non-equilibrium stresses from kinetic theory compare to NS predictions in jet impingement?
• RQ4 Can kinetic simulations reveal significant discrepancies in engineering-relevant surface quantities not captured by continuum turbulence models?

主要发现

• NS-based predictions under NS-SST underpredict surface shear stress by about 25–30% relative to the kinetic solution in dominant regions.
• NS-SST underpredicts peak surface heat flux by roughly 50% and decays more rapidly downstream compared with the Boltzmann solution.
• Non-equilibrium (Boltzmann) stresses become locally dominant where NS shear stress approaches zero due to sign reversals, revealing constitutive degeneracy.
• Direct Boltzmann simulations show localized regions where higher-order kinetic effects govern stress balance despite weak overall rarefaction.
• Degeneracy mechanism explains why weak rarefaction can drive large errors in bulk turbulence predictions in inhomogeneous, high-speed flows.

Figure 2: Direct numerical simulation of the Boltzmann equation using the transient GSIS solver in turbulent-model-free mode [ Zeng2023GSIS ] . (a,b) The NS and Boltzmann shear stress, and their relative strength. (c) The Reynolds shear stress $R_{12}$ and the turbulence production term $\text{Prod}