On solving the 3-D phase field equations by employing a parallel-adaptive mesh refinement (Para-AMR) algorithm

An algorithm comprising adaptive mesh refinement (AMR) and parallel (Para-) computing capabilities was developed to efficiently solve the coupled phase field equations in 3-D. The AMR was achieved based on a gradient criterion and the point clustering algorithm introduced by Berger (1991). To reduce the time for mesh generation, a dynamic regridding approach was developed based on the magnitude of the maximum phase advancing velocity. Local data at each computing process was then constructed and parallel computation was realized based on the hierarchical grid structure created during the AMR. Numerical tests and simulations on single and multi-dendrite growth were performed and results show that the proposed algorithm could shorten the computing time for 3-D phase field simulation for about two orders of magnitude and enable one to gain much more insight in understanding the underlying physics during dendrite growth in solidification.