TIME-STEPPING BOUNDARY-ELEMENT METHOD APPLIED TO 2-D TRANSIENT HEAT-CONDUCTION PROBLEMS

This paper is concerned with a new boundary element method based on th e time-stepping approximation of the time derivative in the governing differential equation. The reduced differential equation at an arbitra ry time step is transferred into an equivalent boundary integral equat ion, and it is solved in a step-by-step manner by means of the standar d boundary element method. The boundary integral formulation is presen ted in detail, and its numerical implementation is used to develop a c omputer code for two-dimensional transient heat conduction problems in isotropic, homogeneous media. The computer code developed is applied to several example problems which demonstrate the effectiveness of the proposed solution procedure. The paper also demonstrates how to deter mine an appropriate time step under a given boundary element mesh by u sing the charts of relationship between the diffusion number and the b oundary element mesh obtained by example computations.