Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

Mohamed, M.S.; Seaid, M.; Trevelyan, J.; Laghrouche, O.

Abstract

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.

Citation

Mohamed, M., Seaid, M., Trevelyan, J., & Laghrouche, O. (2013). Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media. Journal of Computational Physics, 251, 81-101. https://doi.org/10.1016/j.jcp.2013.05.030

• Journal Article Type: Article
• Acceptance Date: May 15, 2013
• Publication Date: Oct 15, 2013
• Deposit Date: Aug 30, 2013
• Publicly Available Date: Nov 30, 2015
• Journal: Journal of Computational Physics
• Print ISSN: 0021-9991
• Electronic ISSN: 1090-2716
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 251
• Pages: 81-101
• DOI: https://doi.org/10.1016/j.jcp.2013.05.030
• Keywords: Finite-element method, Partition-of-unity method, Transient conduction–radiation problems, Simplified P1 approximation, Radiative heat transfer.
• Public URL: https://durham-repository.worktribe.com/output/1471159