A parabolic approximation scheme for multi-phase-filed simulation of non-isothermal solidification

A parabolic approximation scheme is proposed to implement the multi-phase-filed simulation of non-isothermal solidification. Based on the second-order fitting of free energy density function, this scheme constructs an explicit expression for the calculation of phase compositions, which is more efficient than the traditional Newton's iteration scheme used in the Kim-Kim-Suzuki model. As an application example of this numeral scheme, the peritectic solidification of Ti-Al alloy is simulated to present the coupling of multi-phase field and concentration field, which reveals the non-isothermal evolution principle of microstructure and micro-segregation. The present study not only improves the calculation efficiency through a new numeral scheme, but also contributes to the understanding of the thermodynamics and kinetics of Ti-Al peritectic solidification.