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PreprintCC BY-NC-ND 4.0arXiv

Slow heat-driven flow in a gas of hard disks

  • Amit Kumar
  • Abhishek Dhar
  • Baruch Meerson
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Abstract

We study a slow heat-driven flow in a gas of elastically colliding hard disks confined to a long channel. The initial state consists of two regions with large temperature and density contrasts but nearly equal pressures, leading to a low-Mach-number, nearly isobaric evolution. In the dilute limit, the corresponding isobaric hydrodynamic theory reduces to a previously known ideal-gas description. We extend this theory to finite densities by incorporating a non-ideal equation of state of a hard-disk fluid, and solve the resulting one-dimensional equations numerically. Finite-density effects produce appreciable deviations from the ideal-gas prediction. We then test the theory directly against event-driven molecular dynamics simulations of hard disks and find very good agreement in both the dilute and finite-density regimes. The results provide, to our knowledge, the first particle-level test of isobaric gas dynamics of a strongly inhomogeneous cooling flow.

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Cite

BibTeXRIS
BibTeX
@misc{kumar2026slow,
  title = {{Slow heat-driven flow in a gas of hard disks}},
  author = {Amit Kumar and Abhishek Dhar and Baruch Meerson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.00449},
  eprint = {2607.00449},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.00449},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Slow heat-driven flow in a gas of hard disks
AU  - Amit Kumar
AU  - Abhishek Dhar
AU  - Baruch Meerson
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.00449
UR  - https://arxiv.org/abs/2607.00449
AB  - We study a slow heat-driven flow in a gas of elastically colliding hard disks confined to a long channel. The initial state consists of two regions with large temperature and density contrasts but nearly equal pressures, leading to a low-Mach-number, nearly isobaric evolution. In the dilute limit, the corresponding isobaric hydrodynamic theory reduces to a previously known ideal-gas description. We extend this theory to finite densities by incorporating a non-ideal equation of state of a hard-disk fluid, and solve the resulting one-dimensional equations numerically. Finite-density effects produce appreciable deviations from the ideal-gas prediction. We then test the theory directly against event-driven molecular dynamics simulations of hard disks and find very good agreement in both the dilute and finite-density regimes. The results provide, to our knowledge, the first particle-level test of isobaric gas dynamics of a strongly inhomogeneous cooling flow.
ER  -