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Original Articles

Finite element P1 solution of unsteady thermal flow past a circular cylinder with radiation

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Pages 641-656 | Received 19 Oct 2006, Accepted 04 Dec 2006, Published online: 22 Sep 2010
 

Abstract

We propose a finite element method for solving combined convection and radiation in laminar flow past a circular cylinder. The flow problem is described by the thermal incompressible Navier–Stokes equations subject to a Boussinesq approach. To incorporate radiation into the model we consider a simplified P1 approximation of the radiative transfer equation. The numerical solution of the governing equations is performed by a Galerkin-characteristic method using finite element discretization. The method is accurate and stable for a wide range of optical scales and Reynolds numbers. In addition, the characteristic treatment in the method eliminates most of the numerical difficulties that usually appear in the Eulerian-based methods for convection-dominated problems. Numerical results are presented and comparisons between simulations with and without radiation are also illustrated.

Acknowledgements

The work by M. El-Amrani has been supported by Deutscher Akademischer Austausch Dienst (DAAD) grant A/06/12950. The work by M. Seaïd has been partially supported by Deutschen ForschungsGemeinschaft (DFG) through the SFB568.

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