Modelling high-Mach-number rarefied crossflows past a flat plate using the maximum-entropy moment method

TL;DR

This paper evaluates the effectiveness of 10- and 14-moment maximum-entropy methods in modeling high-Mach-number rarefied crossflows past a flat plate, comparing results with particle-based kinetic solutions across different Knudsen numbers.

Contribution

It demonstrates the capabilities and limitations of maximum-entropy moment methods in accurately predicting shock and wake regions in high-Mach rarefied flows.

Findings

10-moment method accurately predicts shock layer at Kn=0.1

14-moment method captures both shock and wake regions better

Both methods show reduced accuracy at Kn=1 with some unphysical results

Abstract

The 10 and 14-moment maximum-entropy methods are applied to the study of high-Mach-number non-reacting crossflows past a flat plate at large degrees of rarefaction. The moment solutions are compared to particle-based kinetic solutions, showing a varying degree of accuracy. At a Knudsen number of 0.1, the 10-moment method is able to reproduce the shock layer, while it fails to predict the low-density wake region, due to the lack of a heat flux. Conversely, the 14-moment method results in accurate predictions of both regions. At a Knudsen number of 1, the 10-moment method produces unphysical results in both the shock layer and in the wake. The 14-moment method also shows a reduced accuracy, but manages to predict a reasonable shock region, free of unphysical sub-shocks, and in qualitative agreement with the kinetic solution. Accuracy is partially lost in the wake, where the 14-moment method predicts a thin unphysical high-density layer, concentrated on the centreline. An analysis of the velocity distribution functions (VDF) indicates strongly non-Maxwellian shapes, and the presence of distinct particle populations, in the wake, crossing each other at the centreline. The particle-based and the 14-moment method VDFs are in qualitative agreement.