Multiphase-field approach with parabolic approximation scheme

A parabolic approximation scheme is implemented to calculate the phase composition and driving force for the numerical application of multiphase-field model. Using an algorithm of solving linear equations instead of iteration, this scheme is more efficient than the traditional Newton-Raphson method in binary or multi-binary system. In order to verify the rationality of this parabolic approximation scheme, we simulate the peritectic solidification of Fe-C binary alloy as an example of numerical application. The study not only compares the driving forces derived from different schemes, but also reveals the interaction of ferrite, austenite and liquid phase during the isothermal solidification, which proves the practicability of the parabolic approximation scheme.