An L2-stable approximation of the Navier–Stokes convection operator for low-order non-conforming finite elements
✍ Scribed by G. Ansanay-Alex; F. Babik; J. C. Latché; D. Vola
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 565 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0271-2091
- DOI
- 10.1002/fld.2270
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✦ Synopsis
Abstract
We develop in this paper a discretization for the convection term in variable density unstationary Navier–Stokes equations, which applies to low‐order non‐conforming finite element approximations (the so‐called Crouzeix–Raviart or Rannacher–Turek elements). This discretization is built by a finite volume technique based on a dual mesh. It is shown to enjoy an L^2^ stability property, which may be seen as a discrete counterpart of the kinetic energy conservation identity. In addition, numerical experiments confirm the robustness and the accuracy of this approximation; in particular, in L^2^ norm, second‐order space convergence for the velocity and first‐order space convergence for the pressure are observed. Copyright © 2010 John Wiley & Sons, Ltd.