| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 2159 - 2191 | |
| DOI | https://doi.org/10.1051/m2an/2023039 | |
| Published online | 03 July 2023 | |
A posteriori error estimates for the Large Eddy Simulation applied to incompressible fluids
1
Laboratoire de Mathématiques et Applications, Unité de recherche Mathématiques et modélisation, Faculté des sciences, Université Saint-Joseph, B.P. 11-514, Riad El Solh Beyrouth 1107 2050, Liban
2
Université Sorbonne Paris Nord, LAGA, CNRS UMR 7539, Institut Galilée, 99 Av. J.-B. Clément, 93430 Villetaneuse, France
3
Université Paris-Saclay, CEA, Service de Génie Logiciel pour la Simulation, 91191 Gif-sur-Yvette, France
* Corresponding author: ghina_nasserdine@hotmail.com
Received:
24
June
2022
Accepted:
28
April
2023
We study the two dimensional time dependent Large Eddy Simulation method applied to the incompressible Navier–Stokes system with Smagorinsky’s eddy viscosity model and a filter width that depends on the local mesh size. The discrete model is based on the implicit Euler scheme and a conforming finite element method for the time and space discretizations, respectively. We establish a reliable and efficient a posteriori error estimation between the numerical LES solution and the exact solution of the original Navier–Stokes system, which involves three types of error indicators respectively related to the filter and to the discretizations in time and space. Numerical results show the effectiveness of adaptive simulations
Mathematics Subject Classification: 65M50 / 65M15 / 76F65 / 76D05
Key words: Large Eddy Simulation / finite element method / a posteriori estimation
© The authors. Published by EDP Sciences, SMAI 2023
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