Reduced Data-Driven Turbulence Closure for Capturing Long-Term Statistics
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| Format: | Preprint |
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2024
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| _version_ | 1866912108801687552 |
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| author | Hoekstra, Rik Crommelin, Daan Edeling, Wouter |
| author_facet | Hoekstra, Rik Crommelin, Daan Edeling, Wouter |
| contents | We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest (QoIs), with only one unresolved scalar time series per QoI. In contrast to other data-driven surrogates the dimension of the "learning problem" is reduced from an evolving field to one scalar time series per QoI. We use an a-posteriori, nudging approach to find the distribution of the scalar series over time. This approach has the advantage of taking the interaction between the solver and the surrogate into account. A stochastic surrogate parametrization is obtained by random sampling from the found distribution for the scalar time series. Compared to an a-priori trained convolutional neural network, evaluating the new method is computationally much cheaper and gives similar long-term statistics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_14132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduced Data-Driven Turbulence Closure for Capturing Long-Term Statistics Hoekstra, Rik Crommelin, Daan Edeling, Wouter Dynamical Systems Numerical Analysis We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest (QoIs), with only one unresolved scalar time series per QoI. In contrast to other data-driven surrogates the dimension of the "learning problem" is reduced from an evolving field to one scalar time series per QoI. We use an a-posteriori, nudging approach to find the distribution of the scalar series over time. This approach has the advantage of taking the interaction between the solver and the surrogate into account. A stochastic surrogate parametrization is obtained by random sampling from the found distribution for the scalar time series. Compared to an a-priori trained convolutional neural network, evaluating the new method is computationally much cheaper and gives similar long-term statistics. |
| title | Reduced Data-Driven Turbulence Closure for Capturing Long-Term Statistics |
| topic | Dynamical Systems Numerical Analysis |
| url | https://arxiv.org/abs/2407.14132 |