Capturing the influence of intermolecular potential in rarefied gas flows by a kinetic model with velocity-dependent collision frequency

TL;DR

This paper introduces the $ u$-model, a kinetic model with velocity-dependent collision frequency, improving the accuracy of rarefied gas flow simulations by capturing intermolecular potential effects.

Contribution

The $ u$-model incorporates velocity-dependent collision frequency, enhancing the simulation accuracy of rarefied gas flows over traditional models.

Findings

Significantly improved accuracy in shock wave simulations.

Effective in modeling thermal transpiration in micro-flows.

Captures effects of intermolecular potentials better than velocity-independent models.

Abstract

A kinetic model called the $\nu$-model is proposed to replace the complicated Boltzmann collision operator in the simulation of rarefied flows of monatomic gas. The model follows the relaxation-time approximation, but the collision frequency (i.e, inverse relaxation time) is a function of the molecular velocity to reflect part of the collision details of the Boltzmann equation, and the target velocity distribution function (VDF) to which the VDF relaxes is close to that used in the Shakhov model. Based on the numerical simulation of strong non-equilibrium shock waves, a half-theoretical and half-empirical collision frequency is designed for different intermolecular potentials: the $\nu$-model shows significantly improved accuracy, and the underlying mechanism is analysed. The $\nu$-model also performs well in canonical rarefied micro-flows, especially in the thermal transpiration, where the conventional kinetic models with velocity-independent collision frequency lack the capability to distinguish the influence of intermolecular potentials.