Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-modal analysis of spectral element methods: Towards accurate and
  robust large-eddy simulations   We introduce a \textit{non-modal} analysis technique that characterizes the
diffusion properties of spectral element methods for linear
convection-diffusion systems. While strictly speaking only valid for linear
problems, the analysis is devised so that it can give critical insights on two
questions: (i) Why do spectral element methods suffer from stability issues in
under-resolved computations of nonlinear problems? And, (ii) why do they
successfully predict under-resolved turbulent flows even without a
subgrid-scale model? The answer to these two questions can in turn provide
crucial guidelines to construct more robust and accurate schemes for complex
under-resolved flows, commonly found in industrial applications. For
illustration purposes, this analysis technique is applied to the hybridized
discontinuous Galerkin methods as representatives of spectral element methods.
The effect of the polynomial order, the upwinding parameter and the P\'eclet
number on the so-called \textit{short-term diffusion} of the scheme are
investigated. From a purely non-modal analysis point of view, polynomial orders
between $2$ and $4$ with standard upwinding are well suited for under-resolved
turbulence simulations. For lower polynomial orders, diffusion is introduced in
scales that are much larger than the grid resolution. For higher polynomial
orders, as well as for strong under/over-upwinding, robustness issues can be
expected. The non-modal analysis results are then tested against under-resolved
turbulence simulations of the Burgers, Euler and Navier-Stokes equations. While
devised in the linear setting, our non-modal analysis succeeds to predict the
behavior of the scheme in the nonlinear problems considered.

5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: acc-phys