Application of the boundary element method for the numerical modelling of the solidification of cylindrical and spherical castings

From the mathematical point of view the solidification process proceeding i n the domain casting-mould is described by the system of partial differenti al equations and boundary/initial conditions. It should be pointed out that taking into account the complex form of the governing equations and the ph ysical, geometrical, boundary and initial conditions an effective solution can be obtained only using numerical methods. In this paper the combined va riant of the boundary element method called the BEM using discretization in time is applied. In particular the well-known numerical algorithm for doma ins oriented in the cartesian co-ordinate system is considered. In order to adapt the method for numerical simulation of the heat-transfer processes p roceeding in domains oriented in other co-ordinate systems a certain algori thm consisting in the introduction of an artificial source is used. (C) 200 0 Elsevier Science B.V. All rights reserved.