کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
472076 | 698687 | 2013 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A conservative numerical method for the Cahn–Hilliard equation with Dirichlet boundary conditions in complex domains A conservative numerical method for the Cahn–Hilliard equation with Dirichlet boundary conditions in complex domains](/preview/png/472076.png)
In this paper we present a conservative numerical method for the Cahn–Hilliard equation with Dirichlet boundary conditions in complex domains. The method uses an unconditionally gradient stable nonlinear splitting numerical scheme to remove the high-order time-step stability constraints. The continuous problem has the conservation of mass and we prove the conservative property of the proposed discrete scheme in complex domains. We describe the implementation of the proposed numerical scheme in detail. The resulting system of discrete equations is solved by a nonlinear multigrid method. We demonstrate the accuracy and robustness of the proposed Dirichlet boundary formulation using various numerical experiments. We numerically show the total energy decrease and the unconditionally gradient stability. In particular, the numerical results indicate the potential usefulness of the proposed method for accurately calculating biological membrane dynamics in confined domains.
Journal: Computers & Mathematics with Applications - Volume 65, Issue 1, January 2013, Pages 102–115