The BEM application for numerical solution of non-steady and nonlinear thermal diffusion problems - Majchrzak, Ewa; Mochnacki, Bohdan (Computer Assisted Methods in Engineering and Science, 1996)
Application of the boundary element method for approximate solution of non-steady and nonlinear thermal diffusion problems is not possible in a direct way. The fundamental solutions (being a basis of the BEM algorithm) are known only for linear problems-in particular the linear form of the Fourier equation is required. On the other hand, the numerous advantages of the boundary element method are a sufficient justification for the examinations concerning the adaptation of the method in this direction. In the paper, the numerical procedures "linearizing" the typical mathematical model of heat conduction process will be discussed. Combining the basic BEM algorithm for linear Fourier equation with procedures correcting the temporary solutions for successive values of time, we obtain a simple tool which allows us to solve a large class of the practical problems concerning the heat conduction processes. In this paper we will discuss in turn the algorithms called the temperature field correction method (TFCM), the alternating phase truncation method (APTM) and the artificial heat source method (AHSM). In the final part of the paper, some examples of numerical solutions will be presented.