| Issue |
ESAIM: ProcS
Volume 76, 2024
New Trends in Complex Flows 2022
|
|
|---|---|---|
| Page(s) | 20 - 34 | |
| DOI | https://doi.org/10.1051/proc/202476020 | |
| Published online | 11 September 2024 | |
Improved Crouzeix-Raviart scheme for the Stokes and Navier-Stokes problem
1
Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, UMR 8208, MSME, F-77454 Marne-la-Vallée, France
2
Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191 Gif-sur-Yvette, France
3
Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191 Gif-sur-Yvette, France
4
Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191 Gif-sur-Yvette, France
eric.chenier@univ-eiffel.fr
erell.jamelot@cea.fr
christophe.le-potier@cea.fr
andrew.peitavy@cea.fr
The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to approach the space:
The non-conforming Crouzeix-Raviart finite element are convenient since they induce local mass conservation. Moreover they are such that the stability constant of the Fortin operator is equal to 1. This implies that they can easily handle anisotropic mesh. However spurious velocities may appear and damage the approximation.
We propose a scheme here that allows one to reduce the spurious velocities. It is based on a new discretisation for the gradient of pressure based on the symmetric MPFA scheme (finite volume MultiPoint Flux Approximation).
© EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.