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
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。
Abstract: 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.
文章引用：刘思福, 潘明阳. 电荷输运相场模型二阶、线性、解耦、能量稳定的数值格式[J]. 应用数学进展, 2024, 13(2): 806-824. https://doi.org/10.12677/AAM.2024.132078

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