full
search.png

Search

close.png

Cancel

arrow
Volume 37, Issue 1
Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions

Xiangjun Meng, Xuelian Bao & Zhengru Zhang

DOI: 10.4208/cicp.OA-2022-0269

Commun. Comput. Phys., 37 (2025), pp. 137-170.

Published online: 2025-01

Preview Full PDF 309 2483

Cited by

google scholar semantic scholar
Export citation
  • Abstract

We propose a kind of second-order stabilized Crank-Nicolson scheme which can be applied to three types of Cahn-Hilliard model with dynamic boundary conditions. We give the corresponding proof of stability and convergence theoretically which takes the reaction rate dependent dynamic boundary conditions as an example. We verify the effectiveness and universality of our proposed scheme by conducting some typical numerical simulations and comparing with the literature works. It’s found that second-order scheme takes much less CPU time than the first-order scheme to reach the same final time.

  • Keywords

Cahn-Hilliard equation, dynamic boundary conditions, reaction rate, second-order Crank-Nicolson formula, energy stability, convergence analysis.

  • AMS Subject Headings

65M12, 65N12, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-37-137, author = {Meng , XiangjunBao , Xuelian and Zhang , Zhengru}, title = {Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions}, journal = {Communications in Computational Physics}, year = {2025}, volume = {37}, number = {1}, pages = {137--170}, abstract = {

We propose a kind of second-order stabilized Crank-Nicolson scheme which can be applied to three types of Cahn-Hilliard model with dynamic boundary conditions. We give the corresponding proof of stability and convergence theoretically which takes the reaction rate dependent dynamic boundary conditions as an example. We verify the effectiveness and universality of our proposed scheme by conducting some typical numerical simulations and comparing with the literature works. It’s found that second-order scheme takes much less CPU time than the first-order scheme to reach the same final time.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0269}, url = {http://global-sci.org/intro/article_detail/cicp/23783.html} }
TY - JOUR T1 - Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions AU - Meng , Xiangjun AU - Bao , Xuelian AU - Zhang , Zhengru JO - Communications in Computational Physics VL - 1 SP - 137 EP - 170 PY - 2025 DA - 2025/01 SN - 37 DO - http://doi.org/10.4208/cicp.OA-2022-0269 UR - https://global-sci.org/intro/article_detail/cicp/23783.html KW - Cahn-Hilliard equation, dynamic boundary conditions, reaction rate, second-order Crank-Nicolson formula, energy stability, convergence analysis. AB -

We propose a kind of second-order stabilized Crank-Nicolson scheme which can be applied to three types of Cahn-Hilliard model with dynamic boundary conditions. We give the corresponding proof of stability and convergence theoretically which takes the reaction rate dependent dynamic boundary conditions as an example. We verify the effectiveness and universality of our proposed scheme by conducting some typical numerical simulations and comparing with the literature works. It’s found that second-order scheme takes much less CPU time than the first-order scheme to reach the same final time.

Meng , XiangjunBao , Xuelian and Zhang , Zhengru. (2025). Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions. Communications in Computational Physics. 37 (1). 137-170. doi:10.4208/cicp.OA-2022-0269
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard