An efficient direct BEM numerical scheme for phase change problems using Fourier series Original Research Article

ue to the moving boundary nature of the solidification and melting problems, the application of the standard time domain boundary element formulation of the problem presents the difficulty of the numerical evaluation of the history dependence, representing more and more work as time proceeds. In that regard, we present an algorithm based on a Greenʹs function which allows a Fourier representation of the domain integral in the reinitialization scheme of the direct boundary element method formulation of the problem, from which it is possible to carry out the history integration in a recursive manner. To obtain the reinitialization approach, in the integral representation formula, the Greenʹs function corresponding to zero temperature in a box containing the original domain will be used, instead of using the classical free space fundamental solution. This Greenʹs function is given in terms of the original fundamental solution plus a regular solution of the heat equation inside the domain in consideration. It can therefore be used in the integral representation formula of the heat equation (direct formulation) to obtain the solution of a heat problem in such domain. The mentioned Greenʹs function can be obtained by the images method, and the resulting source series can also be rewritten in terms of a double Fourier series, that will be used in the domain integral of the integral representation formula to transform such integral into equivalent surface integrals. In this work a new reinitialization scheme has been