Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Closures in a Simple Model for Turbulent Flows   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 eddy viscosity in 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 optimal forms of the eddy viscosity 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
such optimal eddy viscosities the rate of divergence is significantly reduced
as compared to the Smagorinsky model. By systematically finding {optimal forms
of the eddy viscosity within a certain general class of closure} models,
thisframework can thus provide insights about the fundamental performance
limitations of these models.

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The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th