Solidification problems by the boundary element method

Abstract

This paper elaborates on the analysis and design of the solidification of pure metals. In the first part of this paper, a direct analysis is presented for the motion of the solid-liquid freezing interface and the time-dependent temperature field. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time dependent Green's functions and convolution integrals. Emphasis is placed on two-dimensional examples. The second part of this paper provides a methodology for the solution of an inverse design Stefan problem. A method for controlling the fluxes at the freezing front and its velocity is demonstrated. The BEM in conjunction with a sequential least squares technique are used to solve this ill-posed problem that has important technological applications. The accuracy of the method is illustrated through one-dimensional numerical examples.