On the transmission of floating-point perturbations in flow-dependent filter-width formulations in Large-Eddy Simulation
Abstract
Heterogeneous high--performance computing architectures expose numerical algorithms to perturbations arising from the non--associativity of floating--point arithmetic. In Large--Eddy Simulation (LES), similar numerical effects may become relevant when they affect the filter--width entering the subgrid scale (SGS) model. This work investigates this mechanism for the least--squares (LSQ) based filter--width formulation, focusing on how floating--point effects are generated, transmitted, and coupled with the resolved flow. We show that, for fixed resolved kinematics, the LSQ filter--width is logarithmically non-expansive but not strictly contractive with respect to perturbations of the mesh metrics. Consequently, small disturbances may be transmitted with little attenuation through strongly directional filter-width responses. To mitigate this sensitivity, we introduce a scalar max--min compression of the directional mesh scales together with a bounded modulation based on the resolved velocity gradient. The resulting formulation reroutes floating--point perturbations through the filter-width operator, improving robustness while preserving the flow--dependent character of the original LSQ construction. The framework is assessed on heterogeneous CPU and GPU architectures for flow past a circular cylinder at Re=3900 and the Taylor--Green vortex at Re=1600. In the former, nearly one--to--one transmission of relative metric disturbances can become relevant when the transmitted perturbations interact with shear-layer transition. By contrast, on orthogonal Taylor--Green vortex grids, the accumulation pathway is structurally absent and no comparable macroscopic response develops. These results suggest floating--point sensitivity matters for LES filter--width formulations in heterogeneous computing environments.
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BibTeX
@misc{dalessandro2026transmission,
title = {{On the transmission of floating-point perturbations in flow-dependent filter-width formulations in Large-Eddy Simulation}},
author = {Valerio D'Alessandro and Alessio Piccolo and Matteo Falone and Simone Bnà},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01743},
eprint = {2610.01743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01743},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On the transmission of floating-point perturbations in flow-dependent filter-width formulations in Large-Eddy Simulation
AU - Valerio D'Alessandro
AU - Alessio Piccolo
AU - Matteo Falone
AU - Simone Bnà
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01743
UR - https://arxiv.org/abs/2610.01743
AB - Heterogeneous high--performance computing architectures expose numerical algorithms to perturbations arising from the non--associativity of floating--point arithmetic. In Large--Eddy Simulation (LES), similar numerical effects may become relevant when they affect the filter--width entering the subgrid scale (SGS) model. This work investigates this mechanism for the least--squares (LSQ) based filter--width formulation, focusing on how floating--point effects are generated, transmitted, and coupled with the resolved flow. We show that, for fixed resolved kinematics, the LSQ filter--width is logarithmically non-expansive but not strictly contractive with respect to perturbations of the mesh metrics. Consequently, small disturbances may be transmitted with little attenuation through strongly directional filter-width responses. To mitigate this sensitivity, we introduce a scalar max--min compression of the directional mesh scales together with a bounded modulation based on the resolved velocity gradient. The resulting formulation reroutes floating--point perturbations through the filter-width operator, improving robustness while preserving the flow--dependent character of the original LSQ construction. The framework is assessed on heterogeneous CPU and GPU architectures for flow past a circular cylinder at Re=3900 and the Taylor--Green vortex at Re=1600. In the former, nearly one--to--one transmission of relative metric disturbances can become relevant when the transmitted perturbations interact with shear-layer transition. By contrast, on orthogonal Taylor--Green vortex grids, the accumulation pathway is structurally absent and no comparable macroscopic response develops. These results suggest floating--point sensitivity matters for LES filter--width formulations in heterogeneous computing environments.
ER -