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- W2896389968 abstract "In this work we introduce a computational framework for determining optimal closures of the eddy-viscosity type for Large-Eddy Simulations (LES) of a broad class of PDE models, such as the Navier-Stokes equation. This problem is cast in terms of {PDE-constrained} optimization where an error functional representing the misfit between the target and predicted observations is minimized with respect to the functional form of the closure relation. Since this leads to a PDE optimization problem with a nonstandard structure, the solution is obtained computationally with a flexible and efficient gradient approach relying on a combination of modified adjoint-based analysis and Sobolev gradients. By formulating this problem in the continuous setting we are able to determine the optimal closure relations in a very general form subject only to some minimal assumptions. The proposed framework is thoroughly tested on a model problem involving the LES of the 1D Kuramoto-Sivashinsky equation, where the optimal closure relations are obtained as generalizations of the standard Smagorinsky model. It is demonstrated that while the solution trajectories corresponding to the DNS and LES still diverge exponentially, with the optimal closures the rate of divergence is significantly reduced as compared to the Smagorinsky model. By systematically finding the best closure within a certain general family of models, this framework can thus provide insights about the fundamental performance limitations of these models." @default.
- W2896389968 created "2018-10-26" @default.
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- W2896389968 date "2018-01-01" @default.
- W2896389968 modified "2023-09-27" @default.
- W2896389968 title "OPTIMAL CLOSURES IN HYDRODYNAMIC MODELS" @default.
- W2896389968 hasPublicationYear "2018" @default.
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