# A Framework for Characterizing Structural Uncertainty in Large-Eddy Simulation Closures

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## Abstract

Motivated by the sizable increase of available computing resources, large-eddy simulation of complex turbulent flow is becoming increasingly popular. The underlying filtering operation of this approach enables to represent only large-scale motions. However, the small-scale fluctuations and their effects on the resolved flow field require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of incertitude that can impact the quantities of interest. The objective of this work is to introduce a framework for the systematic estimation of structural uncertainty in large-eddy simulation closures. In particular, the methodology proposed is independent of the initial model form, computationally efficient, and suitable to general flow solvers. The approach is based on introducing controlled perturbations to the turbulent stress tensor in terms of magnitude, shape and orientation, such that propagation of their effects can be assessed. The framework is rigorously described, and physically plausible bounds for the perturbations are proposed. As a means to test its performance, a comprehensive set of numerical experiments are reported for which physical interpretation of the deviations in the quantities of interest are discussed.

## Keywords

Large-eddy simulation Predictive science Turbulence modeling Uncertainty quantification## Notes

### Acknowledgments

This work was funded by the United States Department of Energy’s (DoE) National Nuclear Security Administration (NNSA) under the Predictive Science Academic Alliance Program (PSAAP) II at Stanford University.

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to help improve the quality of the paper.

### Compliance with Ethical Standards

### Conflict of interests

The authors declare that they have no conflict of interest.

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