相场方程指数时间差分法的能量稳定性分析

Energy Stability Analysis of Exponential Time Difference Method for Phase Field Equation

相场模型已成为计算材料科学领域模拟和预测中尺度水平微观结构演化的一项通用性很强的计算方法。本文针对Allen-Cahn方程、Cahn-Hilliard方程以及它们的耦合模型,介绍了紧致指数时间差分的解法。这种解法相比于显格式、隐格式的求解方案,具备稳定、大时间步长的优势。同时,对于所介绍的紧致指数时间差分法,本文在严格的数学意义的基础上,证明了它们是符合完全离散的能量稳定性原则,并通过数值实验验证了紧致指数时间差分法的能量稳定性、误差以及时间收敛率。

In computational materials science,phase field model has become a general method for simulating and predicting mesoscale microstructural evolution.In this paper,we present compact Exponential Time Difference methods for Allen-Cahn equation,Cahn-Hilliard equation and their coupling model.Compared with explicit and implicit schemes,this method has the advantages of stability and long time step.At the same time,for the compact Exponential Time Difference method introduced in this paper,it is proved that they are in accordance with the principle of fully discrete energy stability on the basis of strict mathematical meaning.And the energy stability,error and time convergence rate of the compact exponential time difference method are verified by numerical experiments.