PreprintCC BY 4.0arXiv
Exact Collision Vertex for Stress and Heat Flux
Abstract
For the hard-sphere Boltzmann equation, we derive an exact nonlinear generating vertex for collisional stress and heat-flux production. The complete two-input Hermite hierarchy for stress resums to a universal traceless tensor times one scalar radial law, while the heat-flux vertex follows from the same law by an exact contraction. Taylor differentiation yields universal bilinear collision tensors with exact stress and heat-flux gradings, without a finite moment closure. DSMC tests, including wall-driven flows and a bimodal Mach-5 shock, recover independently sampled Boltzmann productions and the predicted convergence, while the converged production is independent of the thermal Gaussian foot used for its Hermite representation.
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BibTeX
@misc{karlin2026exact,
title = {{Exact Collision Vertex for Stress and Heat Flux}},
author = {Ilya Karlin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26807},
eprint = {2609.26807},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26807},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Collision Vertex for Stress and Heat Flux
AU - Ilya Karlin
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.26807
UR - https://arxiv.org/abs/2609.26807
AB - For the hard-sphere Boltzmann equation, we derive an exact nonlinear generating vertex for collisional stress and heat-flux production. The complete two-input Hermite hierarchy for stress resums to a universal traceless tensor times one scalar radial law, while the heat-flux vertex follows from the same law by an exact contraction. Taylor differentiation yields universal bilinear collision tensors with exact stress and heat-flux gradings, without a finite moment closure. DSMC tests, including wall-driven flows and a bimodal Mach-5 shock, recover independently sampled Boltzmann productions and the predicted convergence, while the converged production is independent of the thermal Gaussian foot used for its Hermite representation.
ER -