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

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.

Keywords:

• Finite element method
• Flow past a cylinder
• Galerkin-characteristic scheme
• Radiative transfer
• Simplified P₁ model

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.