- PII
- S3034575825010101-1
- DOI
- 10.7868/S3034575825010101
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 89 / Issue number 1
- Pages
- 136-148
- Abstract
- This paper presents a conservative numerical algorithm for solving the Cahn-Hillard equation. A method for linearizing the Cahn-Hillard equation is proposed, and a numerical scheme is constructed based on the control volume method. The implementation of the proposed numerical algorithm is described in detail. The conservativeness of the proposed discrete scheme is verified by numerical simulation. Numerical experiments were carried out.
- Keywords
- уравнение Кана-Хилларда модель фазового поля начально-краевая задача разностные схемы метод контрольного объема
- Date of publication
- 03.02.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 50
References
- 1. Нигматулин Р.И. Основы механики гетерогенных сред. М.: Наука, 1978. 336 с.
- 2. Gueyffier D., Li J., Nadim A. et al. Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows // J. Comput. Phys. 1999. V. 152. P. 423-456.
- 3. Glimm J., Grove J.W., Li X.L. et al. Three-dimensional front tracking // SIAM J. Sci. Comput. 1998. V. 19. P. 703-727.
- 4. Anderson D.M., McFadden G.B., Wheeler A.A. Diffuse-interface methods in fluid mechanics // Ann. Rev. Fluid Mech. 1998. V. 30. P. 139-165.
- 5. Du Q., Feng X.-B. The phase field method for geometric moving interfaces and their numerical approximations // in: Handbook of Numerical Analysis. Vol. 21. Elsevier, 2020. P. 425-508.
- 6. Badalassi V.E., Ceniceros H.D., Banerjee S. Computation of multiphase systems with phase field models // J. Comput. Phys. 2003. V. 190. P. 371-397.
- 7. Cahn J.W., Hilliard J.E. Free energy of a nonuniform system. I. Interfacial free energy // J. of Chem. Phys. 1958. V. 28(2). P. 258-267.
- 8. Miranville A. The Cahn-Hilliard equation: recent advances and applications // SIAM. 2019.
- 9. Lovrić A., Dettmer W., Perić D. Low order finite element methods for the Navier-Stokes-Cahn-Hilliard equations // arXiv preprint. 2019. arXiv:1911.06718
- 10. Choo S.M., Chung S.K. Conservative nonlinear difference scheme for the Cahn-Hilliard equation // Comput. Math. Appl. 1998. V. 36. P. 31-39.
- 11. Choo S.M., Chung S.K., Kim K.I. Conservative nonlinear difference scheme for the Cahn-Hilliard equation // II. Comput. Math. Appl. 2000. V. 39. P. 229-243.
- 12. Elliott C.M. The Cahn-Hilliard model for the kinetics of phase separation // Math. Models for Phase Change Problems. 1989. P. 35-73.
- 13. Eyre D.J. An unconditionally stable one-step scheme for gradient systems // MRS Proc. 1998.
- 14. Патанкар С.В. Численные методы решения задач теплообмена и динамики жидкости. М.: МЭИ, 1984. 145 с.
- 15. Dhaouadi F., Dumbser M., Gavrilyuk S. A first-order hyperbolic reformulation of the Cahn-Hilliard equation // arXiv preprint. 2024. arXiv:2408.03862
- 16. Li Y., Jeong D., Shin J., Kim J. A conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains // Comput.&Math. with Appl. 2013. V. 65 (1). P. 102-115.
- 17. Лифшиц И.М., Слезов В.В. Кинетика осаждения из пересыщенных твердых растворов // ж. Физики и химии твердых тел. 1961. Т. 19 (1-2). С. 35-50.
- 18. Naraigh O.L., Gloster A. A large-scale statistical study of the coarsening rate in models of Ostwald-Ripening // arXiv preprint. 2019. arXiv: 1911.03386.
