Cahn-Hilliard方程的紧致指数时间差分法研究

Study on Compact Exponential Time Difference Method for Cahn-Hilliard Equation

我们将一种快速稳定的紧致指数时间差分法应用于求解Cahn-Hilliard方程,并采用多步逼近法和龙格库塔方法有效地解决了方程中的非线性项带来的稳定问题。通过与经典的半隐式欧拉方法对比,分别对不同体自由能模型和不同扩散迁移率下的相场方程求解进行收敛性测试,验证了算法的正确性和高效性。最后我们用提出的方法对Flory-Huggins模型的粗化率进行研究,得到了与理论预测值一致的结果。

A fast and stabilized compact exponential time difference method is applied to solve the Cahn-Hilliard equation in this paper. The multistep approximation method and Runge-Kutta method are used to deal with the stability problems causing by the stiff nonlinearity in the equation efficiently. We present the convergence tests on solving phase-field equations with difference local free-energy models and difference diffusion mobilities respectively. By comparing with popular stabilized semi-implicit Euler scheme, thecorrectness and high efficiency of the method has been verified. Furthermore, with our method, the research of the coarsening rate of the Flory-Huggins model indicates that the numerical results are consistent with theoretically predicted values.