Study of dendritic growth and coarsening using a 3-D phase field model: Implementation of the Para-AMR algorithm

Abstract

To efficiently solve the coupled phase field equations in 3-D, an algorithm comprising of adaptive mesh refinement (AMR) and parallel (Para-) computing capabilities was developed. Dendritic growth and subsequent coarsening were studied by employing the model to simulate multi-dendrite growth under isothermal conditions. Quantitative comparison including decrease of interface area (S) and nonlinear growing of the characteristic length (ratio between solid volume V and surface area S i.e. V/S) as time was performed between the simulation results and these predicted by the existing theories. In particular, various mechanisms including growth of lower curvature area in expense of higher curvature one, coalescence of neighbouring dendrite arms and groove advancement at the root of higher order arms for dendritic coarsening were identified and successfully revealed via the 3-D phase field simulation. In addition, results showed that the proposed algorithm could greatly shorten the computing time for 3-D phase field simulation and enable one to gain much more insight in understanding the underlying physics during dendrite growth in solidification.