On the transmission of floating-point perturbations in flow-dependent filter-width formulations in Large-Eddy Simulation

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.