Phase Field Instabilities and Adaptive Mesh Refinement

Robert Almgren

Ann S. Almgren


We show that the phase field model, used for numerical simulation of solidification, can possess unphysical stable intermediate states for certain values of the parameters. We demonstrate that these states can be seen in simple computations in one dimension; in two dimensions we use an adaptive mesh refinement algorithm to exhibit appearance of the intermediate states in realistic geometries of dendritic growth.