Modelling of transport phenomena in gases based on quantum scattering

TL;DR

This paper introduces a quantum scattering implementation in the DSMC method for modeling gas transport phenomena across a wide temperature range, demonstrating significant quantum effects at very low temperatures and computational efficiency at higher temperatures.

Contribution

The paper presents a novel quantum scattering approach integrated into DSMC, enabling accurate modeling of gases from 1 K to high temperatures, surpassing classical methods in low-temperature regimes.

Findings

Quantum effects are negligible above 300 K within 0.1% error.

Quantum effects dominate below 300 K, reaching 67% at 1 K.

Quantum approach reduces computational effort compared to classical methods at higher temperatures.

Abstract

A quantum interatomic scattering is implemented in the direct simulation Monte Carlo (DSMC) method applied to transport phenomena in rarefied gases. In contrast to the traditional DSMC method based on the classical scattering, the proposed implementation allows us to model flows of gases over the whole temperature range beginning from 1 K up any high temperature when no ionization happens. To illustrate the new numerical approach, two helium isotopes $^3$He and $^4$He were considered in two canonical problems, namely, heat transfer between two planar surfaces and planar Couette flow. To solve these problems, the ab initio potential for helium is used, but the proposed technique can be used with any intermolecular potential. The problems were solved over the temperature range from 1 K to 3000 K and for two values of the rarefaction parameter 1 and 10. The former corresponds to the transitional regime and the last describes the temperature jump and velocity slip regime. No influence of the quantum effects was detected within the numerical error of 0.1 % for the temperature 300 K and higher. However, the quantum approach requires less computational effort than the classical one in this temperature range. For temperatures lower than 300 K, the influence of the quantum effects exceed the numerical error and reaches 67 % at the temperature of 1 K.