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 in the domain casting-mould is described by the system of partial differential equations and boundary/initial conditions. It should be pointed out that taking into account the complex form of the governing equations and the physical, geometrical, boundary and initial conditions an effective solution can be obtained only using numerical methods. In this paper the combined variant of the boundary element method called the BEM using discretization in time is applied. In particular the well-known numerical algorithm for domains oriented in the cartesian co-ordinate system is considered. In order to adapt the method for numerical simulation of the heat-transfer processes proceeding in domains oriented in other co-ordinate systems a certain algorithm consisting in the introduction of an artificial source is used.