paper.tex

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\title{
Numerical study of extreme mechanical force exerted by a turbulent flow on a bluff body by direct and rare-event sampling techniques
}

\author{Thibault Lestang\aff{1}\aff{2}
  \corresp{\email{thibault.lestang@cs.ox.ac.uk}},
  Freddy Bouchet\aff{1}
  \and Emmanuel L\'evêque\aff{2}}
\affiliation{\aff{1}Univ Lyon, ENS de Lyon, Univ Claude Bernard de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
\aff{2}Univ Lyon, Ecole Centrale de Lyon, Univ Claude Bernard de Lyon, INSA de Lyon, CNRS, Laboratoire de M\'ecanique des Fluides et d'Acoustique, F-69134 Ecully cedex, France}
\begin{document}

\maketitle

\begin{abstract}
	This study investigates, by means of numerical simulations, extreme mechanical force exerted by a turbulent flow impinging on a bluff body, and examines the relevance of two distinct rare-event algorithms to efficiently sample these events.
	%
	The drag experienced by a square obstacle placed in a turbulent channel flow (in two dimensions) is taken as a representative case study.
	%
	Direct sampling shows that extreme fluctuations are closely related to the presence of a strong vortex blocked in the near wake of the obstacle. This vortex is responsible for a significant pressure drop between the forebody and the base of the obstacle, thus yielding a very high value of the drag.
	%
	Two algorithms are then considered to speed up the sampling of such flow scenarii, namely the \ac{ams} and the \ac{gktl} algorithms.
	The general idea behind these algorithms is to replace a long simulation by a set of much shorter ones, running in parallel, with dynamics that are replicated or pruned, according to some specific rules designed to sample large-amplitude events more frequently.  These algorithms have been shown to be relevant for a wide range of problems in statistical physics, computer science, biochemistry.
        The present study is the first application to a fluid-structure interaction problem.
	% allowing the simulation of rare  events otherwise out of reach by direct sampling.
	%
	Practical evidence is given that the fast sweeping time of turbulent fluid structures past the obstacle has a strong influence on the efficiency of the rare-event algorithm.
	%
	While the \ac{ams} algorithm does not yield significant run-time savings as compared to direct sampling, the \ac{gktl} algorithm appears to be effective to sample very efficiently extreme fluctuations of the time-averaged drag and estimate related statistics such as return times.
      Software used for simulations and data processing is available at \url{https://github.com/tlestang/paper_extreme_drag_fluctuations}.
\end{abstract}

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\section{Acknowledgements}
The authors thank Francesco Ragone, Corentin Herbert, Charles-Edouard Bréhier and Eric Simonnet for useful discussions and suggestions on various aspects of this work.
T.L and F.B acknowledge support from the European Research Council under the European Union's seventh Framework Program (FP7/2007-2013 Grant Agreement No. 616811).
Simulations have been performed on the local HPC facilities at École Normale Supérieure de Lyon (PSMN) and École Centrale de Lyon (PMCS2I).
The facilities at PSMN are supported by the Auvergne-Rhône-Alpes region (GRANT CPRT07-13 CIRA) and the national Equip@Meso grant (ANR-10-EQPX-29-01).

\appendix
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\include{./texfiles/appendixB}
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