Moment hierarchy and exact steady-state solutions in a Callaway lattice Boltzmann model for phonon hydrodynamics
Abstract
We analyze the moment hierarchy of a Callaway lattice Boltzmann model for phonon hydrodynamics and derive exact steady-state solutions for a driven planar channel with diffuse walls. The collision operator decomposes the population space into conserved, heat-flux, and fast kinetic sectors, whose coupling through streaming determines the transport response. For the two-dimensional, eight-velocity (D2Q8) lattice Boltzmann model, we derive a fully discrete closure that relates the heat flux to transverse kinetic moments. The higher-order transverse kinetic moment contains both a second-difference term and an explicit contribution from the imposed energy drop. Diffuse-wall population constraints then determine the heat-flux and kinetic-moment profiles without fitted parameters. The resulting solution reproduces the numerical bulk moment amplitudes and wall slip, while an exact wall relation separates the contribution of the higher-order moment from deviations from the leading gradient approximation. Finite-wave-number analysis further resolves the collision-sector mixing associated with longitudinal propagation. These results provide a unified description of collision relaxation, the moment hierarchy, and boundary response within the specified discrete model.
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BibTeX
@misc{saito2026moment,
title = {{Moment hierarchy and exact steady-state solutions in a Callaway lattice Boltzmann model for phonon hydrodynamics}},
author = {Shimpei Saito},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36146},
eprint = {2609.36146},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36146},
}
RIS
TY - UNPB
TI - Moment hierarchy and exact steady-state solutions in a Callaway lattice Boltzmann model for phonon hydrodynamics
AU - Shimpei Saito
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36146
UR - https://arxiv.org/abs/2609.36146
AB - We analyze the moment hierarchy of a Callaway lattice Boltzmann model for phonon hydrodynamics and derive exact steady-state solutions for a driven planar channel with diffuse walls. The collision operator decomposes the population space into conserved, heat-flux, and fast kinetic sectors, whose coupling through streaming determines the transport response. For the two-dimensional, eight-velocity (D2Q8) lattice Boltzmann model, we derive a fully discrete closure that relates the heat flux to transverse kinetic moments. The higher-order transverse kinetic moment contains both a second-difference term and an explicit contribution from the imposed energy drop. Diffuse-wall population constraints then determine the heat-flux and kinetic-moment profiles without fitted parameters. The resulting solution reproduces the numerical bulk moment amplitudes and wall slip, while an exact wall relation separates the contribution of the higher-order moment from deviations from the leading gradient approximation. Finite-wave-number analysis further resolves the collision-sector mixing associated with longitudinal propagation. These results provide a unified description of collision relaxation, the moment hierarchy, and boundary response within the specified discrete model.
ER -