Energy SSP-IMEX Runge-Kutta methods for the Cahn-Hilliard equation
Energy SSP-IMEX Runge-Kutta methods for the Cahn-Hilliard equation
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DOI：
10.1016/j.cam.2015.07.030
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发表时间：
2016-01
期刊：
影响因子：
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通讯作者：
Huailing Song
中科院分区：
文献类型：
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作者：
Huailing Song
我们考虑描述相分离现象的Cahn-Hilliard方程。方程在空间上采用四阶紧致差分格式离散，在时间上采用保强稳定隐-显（IMEX）龙格-库塔方法离散。新方法具有两个显著的特点：（1）由于能量稳定，可以在数值模拟中使用大的时间步长;（2）能量泛函随时间减小。证明了一阶和二阶方法的无条件能量稳定性。数值实验证明所提出的方法的性能。
We consider the Cahn–Hilliard equation, which describes phase separation phenomenon. The equation is discretized by using a fourth-order compact difference scheme in space and strong-stability-preserving (SSP) implicit–explicit (IMEX) Runge–Kutta methods in time. The new methods have two distinct features: (1) the large time steps can be used in the numerical simulation because the energy is stable, and (2) the energy functional decreases by time. Unconditional energy-stability of first-order and second-order methods are proved. Numerical experiments are given to demonstrate the performance of the proposed methods.