Close Search Advanced
Journals
Resources
About Us
Open Access

High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics

High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics
Preview
Add to basket

Year:    2019

Author:    Jon Matteo Church, Zhenlin Guo, Peter K. Jimack, Anotida Madzvamuse, Keith Promislow, Brian Wetton, Steven M. Wise, Fengwei Yang

Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 947–972

Abstract

There is a large literature of numerical methods for phase field models from materials science. The prototype models are the Allen-Cahn and Cahn-Hilliard equations. We present four benchmark problems for these equations, with numerical results validated using several computational methods with different spatial and temporal discretizations. Our goal is to provide the scientific community with a reliable reference point for assessing the accuracy and reliability of future software for this important class of problem.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0006

Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 947–972

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Allen-Cahn Cahn-Hilliard phase field benchmark computation.

Author Details

Jon Matteo Church

Zhenlin Guo

Peter K. Jimack

Anotida Madzvamuse

Keith Promislow

Brian Wetton

Steven M. Wise

Fengwei Yang

  1. Efficient numerical approaches with accelerated graphics processing unit (GPU) computations for Poisson problems and Cahn-Hilliard equations

    Orizaga, Saulo | Fabien, Maurice | Millard, Michael

    AIMS Mathematics, Vol. 9 (2024), Iss. 10 P.27471

    https://doi.org/10.3934/math.20241334 [Citations: 0]

  2. IMEX methods for thin-film equations and Cahn–Hilliard equations with variable mobility

    Orizaga, Saulo | Witelski, Thomas

    Computational Materials Science, Vol. 243 (2024), Iss. P.113145

    https://doi.org/10.1016/j.commatsci.2024.113145 [Citations: 1]

  3. Linear energy stable and maximum principle preserving semi-implicit scheme for Allen–Cahn equation with double well potential

    Wang, Xiuhua | Kou, Jisheng | Gao, Huicai

    Communications in Nonlinear Science and Numerical Simulation, Vol. 98 (2021), Iss. P.105766

    https://doi.org/10.1016/j.cnsns.2021.105766 [Citations: 39]

  4. A general framework to derive linear, decoupled and energy-stable schemes for reversible-irreversible thermodynamically consistent models

    Zhao, Jia

    Computers & Mathematics with Applications, Vol. 110 (2022), Iss. P.91

    https://doi.org/10.1016/j.camwa.2021.12.011 [Citations: 7]

  5. A Systematic Study of a Droplet Breakup Process in Decaying Homogeneous Isotropic Turbulence Using a Mesoscopic Simulation Approach

    Lai, Jun | Chen, Tao | Zhang, Shengqi | Xiao, Zuoli | Chen, Shiyi | Wang, Lian-Ping

    SSRN Electronic Journal, Vol. (2022), Iss.

    https://doi.org/10.2139/ssrn.4182148 [Citations: 0]

  6. Some algorithms for the mean curvature flow under topological changes

    Bousquet, Arthur | Li, Yukun | Wang, Guanqian

    Computational and Applied Mathematics, Vol. 40 (2021), Iss. 4

    https://doi.org/10.1007/s40314-021-01494-7 [Citations: 1]

  7. Numerical simulation and analysis of the Swift–Hohenberg equation by the stabilized Lagrange multiplier approach

    Yang, Junxiang | Kim, Junseok

    Computational and Applied Mathematics, Vol. 41 (2022), Iss. 1

    https://doi.org/10.1007/s40314-021-01726-w [Citations: 3]

  8. A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility

    Hou, Dianming | Ju, Lili | Qiao, Zhonghua

    Mathematics of Computation, Vol. 92 (2023), Iss. 344 P.2515

    https://doi.org/10.1090/mcom/3843 [Citations: 8]

  9. Energy stable L2 schemes for time-fractional phase-field equations

    Quan, Chaoyu | Wang, Boyi

    Journal of Computational Physics, Vol. 458 (2022), Iss. P.111085

    https://doi.org/10.1016/j.jcp.2022.111085 [Citations: 15]

  10. Structure-preserving discretization of a coupled Allen-Cahn and heat equation system

    Bendimerad-Hohl, Antoine | Haine, Ghislain | Matignon, Denis | Maschke, Bernhard

    IFAC-PapersOnLine, Vol. 55 (2022), Iss. 18 P.99

    https://doi.org/10.1016/j.ifacol.2022.08.037 [Citations: 6]

  11. A first-order computational algorithm for reaction-diffusion type equations via primal-dual hybrid gradient method

    Liu, Shu | Liu, Siting | Osher, Stanley | Li, Wuchen

    Journal of Computational Physics, Vol. 500 (2024), Iss. P.112753

    https://doi.org/10.1016/j.jcp.2024.112753 [Citations: 1]

  12. Solving phase-field models in the tensor train format to generate microstructures of bicontinuous composites

    Risthaus, Lennart | Schneider, Matti

    Applied Numerical Mathematics, Vol. 178 (2022), Iss. P.262

    https://doi.org/10.1016/j.apnum.2022.04.002 [Citations: 3]

  13. Linear relaxation schemes for the Allen–Cahn-type and Cahn–Hilliard-type phase field models

    Jiang, Maosheng | Zhao, Jia

    Applied Mathematics Letters, Vol. 137 (2023), Iss. P.108477

    https://doi.org/10.1016/j.aml.2022.108477 [Citations: 13]

  14. Benchmark Problems for the Numerical Schemes of the Phase‐Field Equations

    Hwang, Youngjin | Lee, Chaeyoung | Kwak, Soobin | Choi, Yongho | Ham, Seokjun | Kang, Seungyoon | Yang, Junxiang | Kim, Junseok | Villatoro, Francisco R.

    Discrete Dynamics in Nature and Society, Vol. 2022 (2022), Iss. 1

    https://doi.org/10.1155/2022/2751592 [Citations: 6]

  15. An explicit stable finite difference method for the Allen–Cahn equation

    Lee, Chaeyoung | Choi, Yongho | Kim, Junseok

    Applied Numerical Mathematics, Vol. 182 (2022), Iss. P.87

    https://doi.org/10.1016/j.apnum.2022.08.006 [Citations: 10]

  16. A systematic study of a droplet breakup process in decaying homogeneous isotropic turbulence using a mesoscopic simulation approach

    Lai, Jun | Chen, Tao | Zhang, Shengqi | Xiao, Zuoli | Chen, Shiyi | Wang, Lian-Ping

    Journal of Turbulence, Vol. 23 (2022), Iss. 11-12 P.567

    https://doi.org/10.1080/14685248.2022.2146700 [Citations: 0]

  17. A Variational Lagrangian Scheme for a Phase-Field Model: A Discrete Energetic Variational Approach

    Liu, Chun | Wang, Yiwei

    SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 6 P.B1541

    https://doi.org/10.1137/20M1326684 [Citations: 12]

  18. A Third Order Exponential Time Differencing Numerical Scheme for No-Slope-Selection Epitaxial Thin Film Model with Energy Stability

    Cheng, Kelong | Qiao, Zhonghua | Wang, Cheng

    Journal of Scientific Computing, Vol. 81 (2019), Iss. 1 P.154

    https://doi.org/10.1007/s10915-019-01008-y [Citations: 75]

  19. Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential

    Wang, Xiuhua | Kou, Jisheng | Cai, Jianchao

    Journal of Scientific Computing, Vol. 82 (2020), Iss. 2

    https://doi.org/10.1007/s10915-020-01127-x [Citations: 30]

  20. Quantifying and eliminating the time delay in stabilization exponential time differencing Runge–Kutta schemes for the Allen–Cahn equation

    Zhang, Hong | Liu, Lele | Qian, Xu | Song, Songhe

    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 58 (2024), Iss. 1 P.191

    https://doi.org/10.1051/m2an/2023101 [Citations: 2]

  21. On an efficient numerical procedure for the Functionalized Cahn-Hilliard equation

    Orizaga, Saulo | Ifeacho, Ogochukwu | Owusu, Sampson

    AIMS Mathematics, Vol. 9 (2024), Iss. 8 P.20773

    https://doi.org/10.3934/math.20241010 [Citations: 1]
  22. Geometric Science of Information

    Structure-preserving Discretization of the Cahn-Hilliard Equations Recast as a Port-Hamiltonian System

    Bendimerad-Hohl, Antoine | Haine, Ghislain | Matignon, Denis

    2023

    https://doi.org/10.1007/978-3-031-38299-4_21 [Citations: 0]

  23. A Simple Benchmark Problem for the Numerical Methods of the Cahn–Hilliard Equation

    Li, Yibao | Lee, Chaeyoung | Wang, Jian | Yoon, Sungha | Park, Jintae | Kim, Junseok | De la Sen, Manuel

    Discrete Dynamics in Nature and Society, Vol. 2021 (2021), Iss. P.1

    https://doi.org/10.1155/2021/8889603 [Citations: 3]

  24. A revisit of the energy quadratization method with a relaxation technique

    Zhao, Jia

    Applied Mathematics Letters, Vol. 120 (2021), Iss. P.107331

    https://doi.org/10.1016/j.aml.2021.107331 [Citations: 29]

  25. Nonsmooth data error estimates for fully discrete finite element approximations of semilinear parabolic equations in Banach space

    Wang, Wansheng | Li, Jinping | Jin, Chengyu

    Journal of Computational and Applied Mathematics, Vol. 448 (2024), Iss. P.115939

    https://doi.org/10.1016/j.cam.2024.115939 [Citations: 0]