A FFT-based phase-field framework for simulating dendritic growth in binary alloy

Abstract

In the present study, a Fourier pseudo-spectral-based, phase-field framework is developed to simulate the binary alloy solidification using fixed grids. The motivation behind this proposition of a new model towards overcoming existing limitations is two-fold: firstly, to create a fully validated high-order phase-field model that closely aligns with LKT predictions of tip kinetics across various undercoolings and compositions, and secondly, to achieve accurate simulations using fixed Cartesian meshes with a grid size of order more than unity. In the Fourier pseudo-spectral method, the nonlinear terms of the PF equations are de-aliased using zero padding and high-order Fourier smoothing exponential filters. Accurate growth kinetics during binary alloy solidification are observed despite employing fixed mesh sizes, even when the ratio of grid size to diffuse interface thickness is 1.42. A hybrid, integrating factor (IF)-based, strongly stable third-order Runge-Kutta method (SSPRK3) is implemented to obtain improved temporal stability at high Lewis numbers. A novel scaling relationship between dimensionless tip velocity and undercooling is obtained from the growth of a four-arm equiaxed dendrite at different levels of undercooling. The growth of several randomly oriented dendrites is also accurately simulated without using any mesh refinement schemes. Likewise, the tip velocity closely matched the LKT predictions at dilute concentrations at the boundary. Furthermore, the effects of the coupling parameter and the anti-trapping term on dendritic growth kinetics are explored. Overall, the proposed FFT-based framework is expected to capture the crystals' global chemical wave features precisely with fewer points per wavelength (PPW) and has the potential to be scaled up for large-scale simulations.