A Fourier spectral method for fractional-in-space Cahn-Hilliard equation

作者：Weng, Zhifeng; Zhai, Shuying^*; Feng, Xinlong

来源：Applied Mathematical Modelling, 2017, 42: 462-477.

DOI：10.1016/j.apm.2016.10.035

• Fractional-in-space Cahn-Hilliard equation
• Periodic and Neumann boundary conditions
• Spectral method
• Crank-Nicolson scheme
• Unconditionally energy stable

In this paper, a fractional extension of the Cahn-Hilliard (CH) phase field model is proposed, i.e. the fractional-in-space CH equation. The fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case. An unconditionally energy stable Fourier spectral scheme is developed to solve the fractional equation with periodic or Neumann boundary conditions. This method is of spectral accuracy in space and of second-order accuracy in time. The main advantages of this method are that it yields high precision and high efficiency. Moreover, an extra stabilizing term is added to obey the energy decay property while maintaining accuracy and simplicity. Numerical experiments are presented to confirm the accuracy and effectiveness of the proposed method.

• 出版日期2017-2
• 单位华侨大学; 新疆大学