Probabilistic data-driven turbulence closure modeling by assimilating statistics
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916659964411904 |
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| author | Ephrati, Sagy |
| author_facet | Ephrati, Sagy |
| contents | A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data assimilation methods. The method requires a posteriori measured data to define stochastic flow perturbations, which are combined with a Bayesian statistical correction enforcing user-specified statistics extracted from high-fidelity flow snapshots. Thus, it enables computationally cheap ensemble simulations by combining knowledge of the local integration error and knowledge of desired flow statistics. A model example is given for two-dimensional Rayleigh-Bénard convection at Rayleigh number $\mathit{Ra}=10^{10}$, incorporating stochastic perturbations and an ensemble Kalman filtering step in a non-intrusive way. Physical flow dynamics are obtained, whilst kinetic energy spectra and heat flux are accurately reproduced in long-time ensemble forecasts on coarse grids. The model is shown to produce accurate results with as few as 20 high-fidelity flow snapshots as input data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic data-driven turbulence closure modeling by assimilating statistics Ephrati, Sagy Fluid Dynamics 37M05, 37N10, 76F35, 76F55, 76F65, 62P35 A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data assimilation methods. The method requires a posteriori measured data to define stochastic flow perturbations, which are combined with a Bayesian statistical correction enforcing user-specified statistics extracted from high-fidelity flow snapshots. Thus, it enables computationally cheap ensemble simulations by combining knowledge of the local integration error and knowledge of desired flow statistics. A model example is given for two-dimensional Rayleigh-Bénard convection at Rayleigh number $\mathit{Ra}=10^{10}$, incorporating stochastic perturbations and an ensemble Kalman filtering step in a non-intrusive way. Physical flow dynamics are obtained, whilst kinetic energy spectra and heat flux are accurately reproduced in long-time ensemble forecasts on coarse grids. The model is shown to produce accurate results with as few as 20 high-fidelity flow snapshots as input data. |
| title | Probabilistic data-driven turbulence closure modeling by assimilating statistics |
| topic | Fluid Dynamics 37M05, 37N10, 76F35, 76F55, 76F65, 62P35 |
| url | https://arxiv.org/abs/2408.14838 |