Reduced Data-Driven Turbulence Closure for Capturing Long-Term Statistics
<|reference_start|>Reduced Data-Driven Turbulence Closure for Capturing Long-Term Statistics: 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.<|reference_end|>
@article{hoekstra2024reduced,
    title={Reduced Data-Driven Turbulence Closure for Capturing Long-Term
  Statistics},
    author={Rik Hoekstra, Daan Crommelin, Wouter Edeling},
    journal={Computers & Fluids 285(2024)106469},
    year={2024},
    doi={10.1016/j.compfluid.2024.106469},
    archivePrefix={arXiv},
    eprint={2407.14132},
    primaryClass={math.DS cs.NA math.NA}
}