Second order accuracy in phase field modeling of normal grain growth

The first and second order accuracy of phase field modeling of normal grain growth is investigated using asymptotic analysis. It is found that the model can achieve first order accuracy but fails to gain second order accuracy. The deviation in second order accuracy is proportional to the inverse of interface thickness so that phase field simulation approaches the sharp interface prediction as interface thickness increases. This result is confirmed by comparison of phase field simulation and analytical solutions, and it well explains the effect of interface thickness on phase field simulation of grain growth observed in previous work.