A fully implicit method for simulation of the one-dimensional solidification of a binary alloy

A finite difference method is developed which overcomes the difficulties of the disparate time scales and small solute diffusion layers inherent to one-dimensional models for the solidification of binary alloys. The boundary immobilization method applied with a coordinate transformation which stretches the solute boundary layer adjacent to the interface is combined with centred difference approximations to generate a set of ordinary differential equations for the solute and temperature fields and the melt/solid interface location. Numerical integration by a variable step-size fully-implicit trapezoid method is compared to an explicit Adams-Bashforth predictor-corrector technique. The implicit method is found to be from two to twelve times more efficient when the Lewis number (the ratio of mass to thermal diffusivities) is small, as is typically the case for metals and semiconductors.