Adaptive finite element approximation of coupled flow and transport problems with applications in heat transfer

✍ Scribed by Mats G. Larson; Robert Söderlund; Fredrik Bengzon

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 581 KB
• Volume: 57
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1818

✦ Synopsis

Abstract

In this paper we develop an adaptive finite element method for heat transfer in incompressible fluid flow. The adaptive method is based on an a posteriori error estimate for the coupled problem, which identifies how accurately the flow and heat transfer problems must be solved in order to achieve overall accuracy in a specified goal quantity. The a posteriori error estimate is derived using duality techniques and is of dual weighted residual type. We consider, in particular, an a posteriori error estimate for a variational approximation of the integrated heat flux through the boundary of a hot object immersed into a cooling fluid flow. We illustrate the method on some test cases involving three‐dimensional time‐dependent flow and transport. Copyright © 2008 John Wiley & Sons, Ltd.