电荷输运相场模型二阶、线性、解耦、能量稳定的数值格式  

A Second-Order, Linear, Decoupled and Energy Stable Numerical Scheme for the Phase Field Model with Charge Transport

作　　者：刘思福 潘明阳 

机构地区：[1]河北工业大学理学院,天津

出　　处：《应用数学进展》2024年第2期806-824,共19页Advances in Applied Mathematics

摘　　要：本文对电荷输运相场模型构造了一种新的二阶精度、 线性、 解捐、 无条件能量稳定的时间步进数 值格式。 首先,通过引入一个具有零能量贡献特征的常微分方程处理非线性捐合项。 其次,结合 标量辅助变量法处理 Cahn-Hilliard 方程中非线性势函数。 时间离散采用二阶向后差分公式,我 们严格证明了该格式下的无条件能量稳定性,并给出详细的解捐实现过程。 最后,通过几个数值 实验验证了所提出方案的准确性和有效性。In this paper, a new second-order accuracy, linear, decoupled and unconditionally energy stable time-stepping numerical scheme is constructed for the phase field mod- el with charge transport. Firstly, an ordinary differential equation with zero energy contribution feature is introduced to handle the nonlinear coupling terms. Second- ly, the scalar auxiliary variable method is used to deal with the nonlinear potential function in the Cahn-Hilliard equation. The second-order backward differentiation formula is used for temporal discretization. We strictly prove the unconditional ener- gy stability of the proposed scheme and provide a detailed decoupling implementation process. Finally, several numerical experiments are carried out to verify the accuracy and effectiveness of the proposed scheme.

关 键 词：相场模型 标量辅助变量法 无条件能量稳定性 有限差分 

分 类 号：O17[理学—数学]