An efficient Pseudo-spectral based phase field method for dendritic solidification

Abstract

In the current study, Fourier Pseudo-spectral based dealiasing scheme Random Phase Shift Method (RPSM) using the RK4 temporal scheme is implemented for simulating some benchmark problems of Phase Field based pure metal solidification. This high-resolution scheme is capable of resolving the thin solid-liquid interface accurately without using Adaptive Mesh Refinement (AMR) algorithm even using just adequate number of grid points. Both the conservative and non-conservative forms of the Phase Field equations are studied. It is found that the conservative RPSM scheme gives better computational performances as indicated by the lower values of average CPU time and different error norms calculated for the Phase Field variable. The RPSM based Phase Field model is applied for simulating dendritic solidification and it is found that dendrite shape and dimensionless tip velocity agree well with the existing literature. The RK4 based RPSM scheme is also compared with a 10th order exponential Fourier smoothing Filter in the evolution of four arm dendritic structure and it is observed that the conservative Phase Field equations with filtering scheme display numerical instabilities at later simulation time, while both forms of the RPSM scheme show stable and accurate solutions. Subsequently, the capability of the RPSM based Phase Field model in simulating microstructure evolution consisting of multiple dendrites with random location and orientation is demonstrated. The present study shows that the RPSM based Phase Field model computes dendritic growth accurately and efficiently.