Application of BEM and sensitivity analysis to the solution of the governing diffusion–convection equation for a continuous casting process

Abstract

This paper presents a two-dimensional diffusion–convection boundary problem which models a continuous casting process of a pure substance (e.g. copper). The boundary problem is formulated for both liquid and solid subdomains separated by a phase change front. Its location is unknown and has to be updated during the iteration process utilising the so-called front tracking algorithm. The solution procedure is based on the Boundary Element Method and involves the total derivative of the temperature and relevant sensitivity coefficients to find a correct position of the phase change front. In order to considerably reduce the number of degrees of freedom in the front tracking algorithm, the position and shape of the phase change front is interpolated by a small number of Bezier segments. Numerical examples are included to demonstrate the main features of the developed algorithms.