Consistent closure modeling in large eddy simulations by direct approximation of the filtered advection term
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910054208241664 |
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| author | Hausmann, Max van Wachem, Berend |
| author_facet | Hausmann, Max van Wachem, Berend |
| contents | This article addresses the widely overlooked conceptual inconsistency of the large eddy simulation (LES) framework, namely that the commonly used advection term introduces higher wave numbers in the filtered Navier-Stokes equations than consistent with the definition of a filtered equation. It is explained how this inconsistency is the reason that flux limiters, stabilization terms, or dealiasing is often required and that the LES solution is typically mesh dependent. A consistent alternative is the direct approximation of the filtered advection term, for which we derive an exact expression based on an infinite series expansion with terms of increasing order in the filter width. We show that truncating the series expansion after few terms gives an expression that is highly correlated with the filtered advection term and a suitable LES model. A posteriori studies with decaying turbulence and a turbulent shear flow are conducted that reveal that the proposed approximation of the filtered advection term predicts improved kinetic energy spectra and filtered velocity correlations compared to classical LES. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_15069 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Consistent closure modeling in large eddy simulations by direct approximation of the filtered advection term Hausmann, Max van Wachem, Berend Fluid Dynamics Computational Physics This article addresses the widely overlooked conceptual inconsistency of the large eddy simulation (LES) framework, namely that the commonly used advection term introduces higher wave numbers in the filtered Navier-Stokes equations than consistent with the definition of a filtered equation. It is explained how this inconsistency is the reason that flux limiters, stabilization terms, or dealiasing is often required and that the LES solution is typically mesh dependent. A consistent alternative is the direct approximation of the filtered advection term, for which we derive an exact expression based on an infinite series expansion with terms of increasing order in the filter width. We show that truncating the series expansion after few terms gives an expression that is highly correlated with the filtered advection term and a suitable LES model. A posteriori studies with decaying turbulence and a turbulent shear flow are conducted that reveal that the proposed approximation of the filtered advection term predicts improved kinetic energy spectra and filtered velocity correlations compared to classical LES. |
| title | Consistent closure modeling in large eddy simulations by direct approximation of the filtered advection term |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2603.15069 |