Year: 2022
Author: Wenbin Chen, Jianyu Jing, Cheng Wang, Xiaoming Wang, Steven M. Wise
Communications in Computational Physics, Vol. 31 (2022), Iss. 1 : pp. 60–93
Abstract
In this paper we propose and analyze a second order accurate numerical scheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the logarithmic nonlinear term, while the expansive term is updated by an explicit second order Adams-Bashforth extrapolation, and an alternate temporal stencil is used for the surface diffusion term. A nonlinear artificial regularization term is added in the numerical scheme, which ensures the positivity-preserving property, i.e., the numerical value of the phase variable is always between -1 and 1 at a point-wise level. Furthermore, an unconditional energy stability of the numerical scheme is derived, leveraging the special form of the logarithmic approximation term. In addition, an optimal rate convergence estimate is provided for the proposed numerical scheme, with the help of linearized stability analysis. A few numerical results, including both the constant-mobility and solution-dependent mobility flows, are presented to validate the robustness of the proposed numerical scheme.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0074
Communications in Computational Physics, Vol. 31 (2022), Iss. 1 : pp. 60–93
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Cahn-Hilliard equation Flory Huggins energy potential positivity preserving energy stability second order accuracy optimal rate convergence estimate.
Author Details
-
Energy dissipative and positivity preserving schemes for large-convection ion transport with steric and solvation effects
Ding, Jie | Wang, Zhongming | Zhou, ShenggaoJournal of Computational Physics, Vol. 488 (2023), Iss. P.112206
https://doi.org/10.1016/j.jcp.2023.112206 [Citations: 3] -
A third-order positivity-preserving and energy stable numerical scheme for the Cahn-Hilliard equation with logarithmic potential
Yuhuan, Li | Jianyu, Jing | Qianqian, Liu | Cheng, Wang | Wenbin, ChenSCIENTIA SINICA Mathematica, Vol. (2024), Iss.
https://doi.org/10.1360/SSM-20223-0014 [Citations: 0] -
A Uniquely Solvable, Positivity-Preserving and Unconditionally Energy Stable Numerical Scheme for the Functionalized Cahn-Hilliard Equation with Logarithmic Potential
Chen, Wenbin | Jing, Jianyu | Wu, HaoJournal of Scientific Computing, Vol. 96 (2023), Iss. 3
https://doi.org/10.1007/s10915-023-02296-1 [Citations: 1] -
Optimal rate convergence analysis of a numerical scheme for the ternary Cahn–Hilliard system with a Flory–Huggins–deGennes energy potential
Dong, Lixiu | Wang, Cheng | Wise, Steven M. | Zhang, ZhengruJournal of Computational and Applied Mathematics, Vol. 415 (2022), Iss. P.114474
https://doi.org/10.1016/j.cam.2022.114474 [Citations: 4] -
A second-order, mass-conservative, unconditionally stable and bound-preserving finite element method for the quasi-incompressible Cahn-Hilliard-Darcy system
Gao, Yali | Han, Daozhi | Wang, XiaomingJournal of Computational Physics, Vol. 518 (2024), Iss. P.113340
https://doi.org/10.1016/j.jcp.2024.113340 [Citations: 0] -
A Positivity-Preserving, Energy Stable BDF2 Scheme with Variable Steps for the Cahn–Hilliard Equation with Logarithmic Potential
Liu, Qianqian | Jing, Jianyu | Yuan, Maoqin | Chen, WenbinJournal of Scientific Computing, Vol. 95 (2023), Iss. 2
https://doi.org/10.1007/s10915-023-02163-z [Citations: 5] -
Convergence analysis of a positivity-preserving numerical scheme for the Cahn-Hilliard-Stokes system with Flory-Huggins energy potential
Guo, Yunzhuo | Wang, Cheng | Wise, Steven | Zhang, ZhengruMathematics of Computation, Vol. 93 (2023), Iss. 349 P.2185
https://doi.org/10.1090/mcom/3916 [Citations: 0] -
Convergence analysis of a second order numerical scheme for the Flory–Huggins–Cahn–Hilliard–Navier–Stokes system
Chen, Wenbin | Jing, Jianyu | Liu, Qianqian | Wang, Cheng | Wang, XiaomingJournal of Computational and Applied Mathematics, Vol. 450 (2024), Iss. P.115981
https://doi.org/10.1016/j.cam.2024.115981 [Citations: 3] -
Linear relaxation method with regularized energy reformulation for phase field models
Zhang, Jiansong | Guo, Xinxin | Jiang, Maosheng | Zhou, Tao | Zhao, JiaJournal of Computational Physics, Vol. 515 (2024), Iss. P.113225
https://doi.org/10.1016/j.jcp.2024.113225 [Citations: 0] -
A parareal exponential integrator finite element method for semilinear parabolic equations
Huang, Jianguo | Ju, Lili | Xu, YuejinNumerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 6
https://doi.org/10.1002/num.23116 [Citations: 0] -
Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations
Huang, Jianguo | Ju, Lili | Xu, YuejinSIAM Journal on Scientific Computing, Vol. 45 (2023), Iss. 4 P.A1545
https://doi.org/10.1137/22M1498127 [Citations: 3] -
EnVarA-FEM for the flux-limited porous medium equation
Liu, Qianqian | Duan, Chenghua | Chen, WenbinJournal of Computational Physics, Vol. 493 (2023), Iss. P.112432
https://doi.org/10.1016/j.jcp.2023.112432 [Citations: 0] -
A Positivity Preserving, Energy Stable Finite Difference Scheme for the Flory-Huggins-Cahn-Hilliard-Navier-Stokes System
Chen, Wenbin | Jing, Jianyu | Wang, Cheng | Wang, XiaomingJournal of Scientific Computing, Vol. 92 (2022), Iss. 2
https://doi.org/10.1007/s10915-022-01872-1 [Citations: 13]