Coexistence of doublon and dendrite structure with phase-field model

Doublon is one of the typical patterns found in crystal growth. It is a pair of symmetry broken fingers. In this paper, we obtain numerically parameter range of coexistence of doublon and dendrite structure with a phase-field model. We perform numerical simulations in a two-dimensional channel, setting small seed of crystal at left-bottom side of the channel as an initial condition. The oscillation of groove of doublon appears in some parameter range even though without perturbation. In other parameter range, both dendrite and doublon make their appearance along same growth direction.