Application of scalar auxiliary variable scheme to phase-field equations

It has been a continuing challenge to carry out simulations at time and spatial scales compatible with practical experimental observations. Here we implement a novel scalar auxiliary variable (SAV) scheme introduced in (Shen et al., 2018) for phase-field equations to drastically improve the numerical accuracy, efficiency and stability. We first bench-marked two representative phase-field method applications involving three-dimensional (3D) grain growth and spinodal phase separation. By implementing the SAV scheme within the state-of-the-art semi-implicit Fourier spectral scheme we achieved an order of magnitude improvement for the single-order-parameter Allen-Cahn equation and at least a 100% improvement for a set of multi-order-parameter Allen-Cahn equations for grain growth problems and the Cahn-Hilliard equation for compositional phase separation. More importantly, the efficiency enhancement of SAV becomes more dramatic as interfaces become sharper. Its application to the growth morphology and kinetics of β’-Mg₇Nd precipitates demonstrates a remarkable improvement of more than 50 times in computational time. This work is expected to further stimulate the applications of phase-field simulations of a broad range of materials processes.