An adaptive mesh refinement scheme for solidification problems

Methods for adaptive mesh refinement, based on a quadtree data structure, have been developed with the specific objective of tracking solid/liquid front movement in two-dimensional solidification problems. These methods include mesh refinement and unrefinement algorithms for the finite element method applied to transient problems. Ana posteriori error estimator is described to locate regions in the finite element mesh needing refinement. One- and two-dimensional example applications are given, showing how the methods can be used to resolve a moving solidification front and its associated boundary layer in binary alloy solidification.