A Complete Set of Grad's Thirteen Regularized Moment Equations

TL;DR

This paper derives a complete set of regularized Grad's thirteen moment equations for rarefied gases using Hermite polynomial approximation and Chapman-Enskog regularization, extending their accuracy to third order in the Knudsen number.

Contribution

It introduces a complete, regularized set of Grad's thirteen moment equations derived from the BGK model, enhancing the accuracy of rarefied gas flow modeling.

Findings

The derived equations are complete and extend Grad's original formulation.

All previous closures are special truncations of the new equations.

Using these equations improves accuracy in gas flow and heat transfer simulations.

Abstract

This paper derives transport equations for medium rarefied gases from the Bhatnagar-Gross-Krook (BGK) model kinetic equation using a Hermite polynomial approximation for the monoatomic gas distribution function. We apply the Chapman-Enskog regularization method to Grad's velocity distribution function that corresponds to his thirteen moment equation, extending these equations to the third order of the Knudsen number. We show that the obtained set of Grad's regularized thirteen moment equations is complete, and that all previously obtained closures for Grad's thirteen moment equations are the sets of truncated equations obtained in this paper. Using the truncated transport equations may lead to losing accuracy in computing gas flows and heat transfer in rarefied gases. The velocity distribution function for the resulting 13 regularized moment equations is presented.