Extensions to the Navier-Stokes-Fourier Equations for Rarefied Transport: Entropy Variable Formulation, Heat Transfer and Dispersion of a Non-Linear Entropy Stable Closure
Abstract
We assess the non-linear version of the Entropy Stable Extension to the Navier-Stokes-Fourier equations which were originally derived in arXiv:2407.17334. Using an identity for the derivative of the inverse of linearized collision operator, we show that the Entropy Stable Extension takes the form of a fourth-order quasi-cubic system of equations when written in entropy variables. Furthermore, we find that the quasi-linear contributions to the extension retain the highest order derivative contributions and the entropy stability of the full extension. This quasi-linear approximation is applied to the stationary heat transfer between parallel plates where we find that a specification of the boundary conditions that interpolates between the continuum and collisions limits can yield temperature profiles that better agree with DSMC predictions than Navier-Stokes-Fourier equations with Smoluchowski boundary conditions, while also giving a heat flux prediction that better agrees with the Sherman-Lees heat flux than the Navier-Stokes-Fourier prediction. We conclude with a brief study of dispersion of plane waves according to the linearized equations in one dimension where we show that all frequency modes are stable and relate this to entropy stability.
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BibTeX
@misc{baidoo2026extensions,
title = {{Extensions to the Navier-Stokes-Fourier Equations for Rarefied Transport: Entropy Variable Formulation, Heat Transfer and Dispersion of a Non-Linear Entropy Stable Closure}},
author = {Frimpong A. Baidoo and Narayana R. Aluru and Thomas J. R. Hughes and Michael R. A. Abdelmalik},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08395},
eprint = {2611.08395},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08395},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Extensions to the Navier-Stokes-Fourier Equations for Rarefied Transport: Entropy Variable Formulation, Heat Transfer and Dispersion of a Non-Linear Entropy Stable Closure
AU - Frimpong A. Baidoo
AU - Narayana R. Aluru
AU - Thomas J. R. Hughes
AU - Michael R. A. Abdelmalik
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08395
UR - https://arxiv.org/abs/2611.08395
AB - We assess the non-linear version of the Entropy Stable Extension to the Navier-Stokes-Fourier equations which were originally derived in arXiv:2407.17334. Using an identity for the derivative of the inverse of linearized collision operator, we show that the Entropy Stable Extension takes the form of a fourth-order quasi-cubic system of equations when written in entropy variables. Furthermore, we find that the quasi-linear contributions to the extension retain the highest order derivative contributions and the entropy stability of the full extension. This quasi-linear approximation is applied to the stationary heat transfer between parallel plates where we find that a specification of the boundary conditions that interpolates between the continuum and collisions limits can yield temperature profiles that better agree with DSMC predictions than Navier-Stokes-Fourier equations with Smoluchowski boundary conditions, while also giving a heat flux prediction that better agrees with the Sherman-Lees heat flux than the Navier-Stokes-Fourier prediction. We conclude with a brief study of dispersion of plane waves according to the linearized equations in one dimension where we show that all frequency modes are stable and relate this to entropy stability.
ER -