An implicit enthalpy solution for phase change problems: with application to a binary alloy solidification

An enthalpy method is developed for analysis of one-dimensional phase change problems under heat conduction. This technique is based on a fixed space grid but a variable time step is used to ensure that the phase front is always on a node point. The resulting numerical solution is implicit in nature and although iteration on the time step is needed at each time level, the tridiagonal matrix algorithm can be utilized within the iterations leading to efficient and accurate solutions. The node-jumping scheme is extended and a numerical solution to the well-known binary solidification model developed. This solution is implicit and performs well in respect to predicting discontinuities in the enthalpy and concentration fields and in predicting smooth non-oscillating temperature and concentration and histories.