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Stabilized finite element method for incompressible flows with high Reynolds number

Abstract : In the following paper, we discuss the exhaustive use and implementation of stabilization finite element methods for the resolution of the 3D time-dependent incompressible Navier–Stokes equations. The proposed method starts by the use of a finite element variational multiscale (VMS) method, which consists in here of a decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. This choice of decomposition is shown to be favorable for simulating flows at high Reynolds number. We explore the behaviour and accuracy of the proposed approximation on three test cases. First, the lid-driven square cavity at Reynolds number up to 50,000 is compared with the highly resolved numerical simulations and second, the lid-driven cubic cavity up to Re = 12,000 is compared with the experimental data. Finally, we study the flow over a 2D backward-facing step at Re = 42,000. Results show that the present implementation is able to exhibit good stability and accuracy properties for high Reynolds number flows with unstructured meshes.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00521881
Contributor : Magalie Prudon <>
Submitted on : Tuesday, September 28, 2010 - 5:33:57 PM
Last modification on : Thursday, September 24, 2020 - 5:22:54 PM

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Elie Hachem, Benjamin Rivaux, Thibaud Kloczko, Hugues Digonnet, Thierry Coupez. Stabilized finite element method for incompressible flows with high Reynolds number. Journal of Computational Physics, Elsevier, 2010, 229 (23), pp.Pages 8643-8665. ⟨10.1016/j.jcp.2010.07.030⟩. ⟨hal-00521881⟩

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