On the entropic property of the Ellipsoidal Statistical model with the Prandtl number below 2/3

TL;DR

This paper investigates the entropic properties of the Ellipsoidal Statistical model with Prandtl numbers below 2/3, showing the H theorem's validity under certain stress anisotropy conditions through numerical tests.

Contribution

It demonstrates that the H theorem can hold for Prandtl numbers below 2/3 if stress anisotropy meets specific criteria, extending the understanding of the model's entropic properties.

Findings

H theorem holds for Pr<2/3 under stress anisotropy conditions

Numerical validation with shock wave and Couette flow simulations

Prandtl number lower bound can be relaxed with stress tensor criteria

Abstract

Entropic property of the Ellipsoidal Statistical model with the Prandtl number Pr below 2/3 is discussed. Although 2/3 is the lower bound of Pr for the H theorem to hold unconditionally, it is shown that the theorem still holds even for $\mathrm{Pr}<2/3$, provided that anisotropy of stress tensor satisfies a certain criterion. The practical tolerance of that criterion is assessed numerically by the strong normal shock wave and the Couette flow problems. A couple of moving plate tests are also conducted.