Bulk-to-Wall Observability in Rarefied Hypersonic Flow: Moment Limits and Incident Half-Range Sufficiency
Abstract
Wall traction in a rarefied gas is a half-range functional of molecules arriving at and leaving a surface, whereas hybrid solvers, moment methods, and learned wall models often transmit only finite full-range moments. We determine which directional information is lost and what restores the wall functional using direct simulation Monte Carlo (DSMC) of Mach-6 flow over three triangular-protrusion orientations. Output-specialized neural networks interpolate a 57-condition DSMC database. A distinct ExtraTrees regression holds learner capacity, auxiliary features, train/test split, and seeds fixed while comparing the primitive state S0, the momentum-flux-augmented state S1, and the heat-flux-augmented state S2. Adding the momentum-flux tensor Pij reduces aggregate pressure error by 31\% but does not make signed shear transferable. An analytic null-space construction supplies the mechanism: strictly positive distributions can share all full-range moments through degree three while producing different pressure and opposite signed shear because the wall kernel selects the incident half space. A finite-distance off-wall ExtraTrees state Soff shows that partial directionality is useful but representation-dependent. Finally, a parameter-free kinetic reconstruction combines the incident half-range wall-arrival state SHR with the prescribed diffuse kernel and agrees with both a same-window DSMC tally sharing the incident events and a separate 40,000-step DSMC wall-tally window. The resulting design principle is direct: a rarefied wall closure must preserve the incident normal--tangential correlations required by the target load rather than merely adding higher full-range moments.
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BibTeX
@misc{lekzian2026bulktowall,
title = {{Bulk-to-Wall Observability in Rarefied Hypersonic Flow: Moment Limits and Incident Half-Range Sufficiency}},
author = {Elyas Lekzian and Ehsan Roohi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.25752},
eprint = {2606.25752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.25752},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bulk-to-Wall Observability in Rarefied Hypersonic Flow: Moment Limits and Incident Half-Range Sufficiency
AU - Elyas Lekzian
AU - Ehsan Roohi
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2606.25752
UR - https://arxiv.org/abs/2606.25752
AB - Wall traction in a rarefied gas is a half-range functional of molecules arriving at and leaving a surface, whereas hybrid solvers, moment methods, and learned wall models often transmit only finite full-range moments. We determine which directional information is lost and what restores the wall functional using direct simulation Monte Carlo (DSMC) of Mach-6 flow over three triangular-protrusion orientations. Output-specialized neural networks interpolate a 57-condition DSMC database. A distinct ExtraTrees regression holds learner capacity, auxiliary features, train/test split, and seeds fixed while comparing the primitive state S_0, the momentum-flux-augmented state S_1, and the heat-flux-augmented state S_2. Adding the momentum-flux tensor P_ij reduces aggregate pressure error by 31\% but does not make signed shear transferable. An analytic null-space construction supplies the mechanism: strictly positive distributions can share all full-range moments through degree three while producing different pressure and opposite signed shear because the wall kernel selects the incident half space. A finite-distance off-wall ExtraTrees state S_off shows that partial directionality is useful but representation-dependent. Finally, a parameter-free kinetic reconstruction combines the incident half-range wall-arrival state S_HR with the prescribed diffuse kernel and agrees with both a same-window DSMC tally sharing the incident events and a separate 40,000-step DSMC wall-tally window. The resulting design principle is direct: a rarefied wall closure must preserve the incident normal--tangential correlations required by the target load rather than merely adding higher full-range moments.
ER -