Evolution of the solidification front of a binary mixture

We perform a numerical study of two-dimensional solidification of a binary alloy. We employ a front-fixing transformation and develop a finite-difference numerical scheme, which is then used to simulate the evolution of an initially planar solidification front. The self-similar solution is taken as a base state for numerical investigation; the parameter choice corresponds to the case when the melt is constitutionally supercooled and the linear instability is expected. The perturbed interface takes the form of traveling waves with nonlinear growth rate, with the increased Stefan number causing the slow-down of solidification. Another important feature is the decay of perturbation when the time t0t0 at which the perturbation is imposed to the self-similar base solution is large enough, despite the fact that the system is expected to be linearly unstable. Finally, we provide a numerical investigation of the lowest value of t0t0 for which the perturbation decays in time and its dependence on Stefan number.