Phase field model for three-dimensional dendritic growth with fluid flow -art. no. 041602

We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-field model on an adaptive finite-element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow problem cou pled to the phase-field method and the semi-implicit approximated projectio n method (SIAPM). We describe a parallel implementation for the algorithm, using the CHARM+ + FEM framework, and demonstrate its efficiency. We introd uce an improved method for extracting dendrite tip position and tip radius, facilitating accurate comparison to theory. We benchmark our results for 2 D dendrite growth with solvability theory and previous results, finding the m to be in good agreement. The physics of dendritic growth with fluid flow in three dimensions is very different from that in two dimensions, and we d iscuss the origin of this behavior.