Fast simulations of a large number of crystals growth in centimeter-scale during alloy solidification via nonlinearly preconditioned quantitative phase-field formula

Ameliorating the computing efficiency is always of importance in phase-field simulations of material microstructure formation and evolution. Borrowing from the nonlinear preconditioning treatment of diffuse interface models, the usual quantitative phase-field model for a binary alloy has been transformed to make it easier to compute accurately. The transformation yields a new variable whose value changes linearly across the interface. The dependences of simulated results of the nonlinearly preconditioned phase-field formula on the interface grid size and the discretization time step have been examined in detail through numerical experiments, including the growth velocity, the radius and the solute concentration of a steady tip. The results show that the new evolution equations are able to be solved on a computational mesh with interface grids 2-4 times coarser than those used in the conventional method. In combination with the front-tracking method to capture the crystallographic orientation of each crystal, the orientation gradient energy is incorporated into the nonlinearly preconditioned phase-field model, which enables simulations of grain boundary behaviors. The algorithm of the distributed parallel finite element method on an adaptive mesh is applied to further raise the computing efficiency. Simulations of multidendrites growth of Al-4 wt.% Cu alloy in undercooled melt cooling down continuously are performed. The results demonstrate that the proposed fast simulation approaches allow quantitative simulations of a large number of dendrites growth on the scale of centimeters or millimeters, respectively in two or three dimensions, just using an ordinary workstation instead of clusters or supercomputers. (C) 2018 Elsevier B.V. All rights reserved.