Abstract
This paper is concerned with a new boundary element method based on the time-stepping approximation of the time derivative in the governing differential equation. The reduced differential equation at an arbitrary time step is transferred into an equivalent boundary integral equation, and it is solved in a step-by-step manner by means of the standard boundary element method. The boundary integral formulation is presented in detail, and its numerical implementation is used to develop a computer 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 determine an appropriate time step under a given boundary element mesh by using the charts of relationship between the diffusion number and the boundary element mesh obtained by example computations.
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