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

参考文献

[1] Pethig, R. (1996) Dielectrophoresis: Using Inhomogeneous AC Electrical Fields to Separate and Manipulate Cells. Critical Reviews in Biotechnology, 16, 331-348.
https://doi.org/10.3109/07388559609147425
[2] Bank, R.E., Rose, D.J. and Fichtner, W. (1983) Numerical Methods for Semiconductor Device Simulation. SIAM Journal on Scientific and Statistical Computing, 4, 416-435.
https://doi.org/10.1137/0904032
[3] Papageorgiou, D.T. (2019) Film Flows in the Presence of Electric Fields. Annual Review of Fluid Mechanics, 51, 155-187.
https://doi.org/10.1146/annurev-fluid-122316-044531
[4] Nielsen, C.P. and Bruus, H. (2015) Sharp-Interface Model of Electrodeposition and Ramified Growth. Physical Review E, 92, Article 042302.
https://doi.org/10.1103/PhysRevE.92.042302
[5] Christiansen, S.H., Munthe-Kaas, H.Z. and Owren, B. (2011) Topics in Structure-Preserving Discretization. Acta Numerica, 20, 1-119.
https://doi.org/10.1017/S096249291100002X
[6] Hu, Z., Wise, S.M., Wang, C. and Lowengrub, J.S. (2009) Stable and Efficient Finite-Difference Nonlinear-Multigrid Schemes for the Phase Field Crystal Equation. Journal of Computational Physics, 228, 5323-5339.
https://doi.org/10.1016/j.jcp.2009.04.020
[7] Liu, C., Shen, J. and Yang, X. (2007) Dynamics of Defect Motion in Nematic Liquid Crystal Flow: Modeling and Numerical Simulation. Communications in Computational Physics, 2, 1184-1198.
[8] Yang, X. (2016) Linear, First and Second-Order, Unconditionally Energy Stable Numerical Schemes for the Phase Field Model of Homopolymer Blends. Journal of Computational Physics, 327, 294-316.
https://doi.org/10.1016/j.jcp.2016.09.029
[9] Shen, J., Xu, J. and Yang, J. (2018) The Scalar Auxiliary Variable (SAV) Approach for Gradient Flows. Journal of Computational Physics, 353, 407-416.
https://doi.org/10.1016/j.jcp.2017.10.021
[10] Yang, X. (2021) On a Novel Fully Decoupled, Second-Order Accurate Energy Stable Numer- ical Scheme for a Binary Fluid-Surfactant Phase-Field Model. SIAM Journal on Scientific Computing, 43, B479-B507.
https://doi.org/10.1137/20M1336734
[11] Chen, Y. and Shen, J. (2016) Efficient, Adaptive Energy Stable Schemes for the Incompressible Cahn-Hilliard Navier-Stokes Phase-Field Models. Journal of Computational Physics, 308, 40- 56.
https://doi.org/10.1016/j.jcp.2015.12.006
[12] Yang, X. (2021) On a Novel Fully-Decoupled, Linear and Second-Order Accurate Numerical Scheme for the Cahn-Hilliard-Darcy System of Two-Phase Hele-Shaw Flow. Computer Physics Communications, 263, Article 107868.
https://doi.org/10.1016/j.cpc.2021.107868

为你推荐



Baidu
map