A framework for large eddy simulation of Burgers turbulence based upon spatial and temporal statistical information

We present a novel theoretical framework that has the potential not only to improve the reliability and computational efficiency of large-eddy simulation (LES) predictions for turbulent flows but also promises to address a major drawback of many existing constructs of LES, namely, inaccurate predictions for the underlying spatiotemporal structure. In our proposed framework, subgrid models are constructed based upon information that is consistent with the underlying spatiotemporal statistics of the flow. Unlike many pre-existing LES approaches, the proposed subgrid models include non-Markovian memory terms whose origins can be related to the optimal prediction formalism. These optimal subgrid models are studied within the context of the forced Burgers equation. Results indicate that the proposed models perform better than standard LES models by virtue of their ability to better preserve the underlying spatiotemporal statistical structure of the flow. Furthermore, the presence of coarse-grained temporal information in our subgrid models allows for faster simulations (resulting in about an order of magnitude reduction in computational time, in comparison to conventional LES) through the use of larger time steps.

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