What does anti-Fourier heat-flux agreement validate? Observability of the fourth-order closure state in a rarefied lid-driven cavity
Abstract
Cold-to-hot heat transfer is a conspicuous non-equilibrium feature of rarefied cavity flows and is often used to judge whether a continuum closure captures higher-order transport. We examine what such agreement actually establishes. The exact heat-flux balance shows that the fourth-order contribution enters only through the divergence of the composite tensor (A_{ij}=R^{\mathrm{cl}}*{ij}+Δδ*{ij}/3). A compactly supported Airy construction yields an infinite-dimensional family of symmetric divergence-free perturbations that preserve the flux-side wall trace. A two-dimensional-physical, three-dimensional-velocity (2D3V) description also leaves the transverse component (A_{zz}) unobserved. Heat flux therefore cannot uniquely identify the underlying fourth-order state. We test the consequences using direct simulation Monte Carlo (DSMC) ensembles and independent regularized 13-moment (R13) and regularized 26-moment (R26) solutions at two rarefaction levels. Counter-gradient transport and the dominant tensorial channel persist under changes in grid and particle number, whereas the local scalar fourth moment and the spatial organization of the counter-gradient region are more sensitive. A finite-particle-corrected fourth-moment audit shows that more than 95% of the resolved R26--DSMC composite-tensor discrepancy at the higher rarefaction lies in the discrete divergence-null space, whereas projected sampling noise hides only about half of its energy. R26 captures the circulation and heat-flux direction more closely than R13, yet the remaining differences concentrate in the wall and corner layers.
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BibTeX
@misc{roohi2026what,
title = {{What does anti-Fourier heat-flux agreement validate? Observability of the fourth-order closure state in a rarefied lid-driven cavity}},
author = {Ehsan Roohi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27892},
eprint = {2609.27892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27892},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - What does anti-Fourier heat-flux agreement validate? Observability of the fourth-order closure state in a rarefied lid-driven cavity
AU - Ehsan Roohi
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27892
UR - https://arxiv.org/abs/2609.27892
AB - Cold-to-hot heat transfer is a conspicuous non-equilibrium feature of rarefied cavity flows and is often used to judge whether a continuum closure captures higher-order transport. We examine what such agreement actually establishes. The exact heat-flux balance shows that the fourth-order contribution enters only through the divergence of the composite tensor (A_{ij}=R^{\mathrm{cl}}*{ij}+Δδ*{ij}/3). A compactly supported Airy construction yields an infinite-dimensional family of symmetric divergence-free perturbations that preserve the flux-side wall trace. A two-dimensional-physical, three-dimensional-velocity (2D3V) description also leaves the transverse component (A_{zz}) unobserved. Heat flux therefore cannot uniquely identify the underlying fourth-order state. We test the consequences using direct simulation Monte Carlo (DSMC) ensembles and independent regularized 13-moment (R13) and regularized 26-moment (R26) solutions at two rarefaction levels. Counter-gradient transport and the dominant tensorial channel persist under changes in grid and particle number, whereas the local scalar fourth moment and the spatial organization of the counter-gradient region are more sensitive. A finite-particle-corrected fourth-moment audit shows that more than 95% of the resolved R26--DSMC composite-tensor discrepancy at the higher rarefaction lies in the discrete divergence-null space, whereas projected sampling noise hides only about half of its energy. R26 captures the circulation and heat-flux direction more closely than R13, yet the remaining differences concentrate in the wall and corner layers.
ER -