Hybrid BEM for the early stage of a 3D unsteady heat diffusion process

Abstract

This article presents a hybrid three dimensional dual reciprocity boundary element method (BEM) for solving the early stage of a 3D time dependent convective heat transfer equation in non-homogeneous media. The method addresses the problem in which the initial distribution of temperature presents a discontinuous jump at the interface between two regions of very dissimilar diffusion coefficients. The goal of this hybrid formulation is to sort out the numerical inconvenience of different time scales and apparent large flux during early time by combining the 3D BEM with a series of 1D semi-analytical profiles of the time dependent heat diffusion equation, employing a two-level finite difference time integration scheme. This article presents the theoretical background, and one 3D test example. The formulation provided offers convenient advantages for relatively large scale models and complex 3D geometries.