The scaled boundary finite element method based on the hybrid quadtree mesh for solving transient heat conduction problems

Abstract

In this paper, a hybrid quadtree mesh is utilized to solve two-dimensional transient heat conduction problems with cracks or inclusions. The current approach developed based on the scaled boundary finite element method (SBFEM) is able to alleviate the hanging node issues typically encountered in the conventional finite element method when using quadtree mesh. Moreover, the present method does not require fundamental solutions, unlike the boundary element method. The formulas of temperature and temperature gradient fields are derived systematically for the insulated crack and the inclusions of different materials with temperature and heat flux boundary conditions. Several examples are presented to demonstrate the validity and stability of SBFEM when solving models with complex geometry and cracks or inclusions.