Adaptive Delaunay triangulation for steady-state and transient heat transfer analyses

Abstract

A finite element method is combined with the Delaunay triangulation and the adaptive remeshing technique to find solutions of both steady-state and transient heat transfer problems. The Delaunay triangulation and the adaptive remeshing technique are explained in detail. The solution accuracy and the effectiveness of the combined procedure are evaluated by heat transfer problems that have exact solutions. These problems include steady-state heat conduction in a square plate subjected to a highly localized surface heating, and a transient heat conduction in a long plate subjected to a moving heat source.