Volume 36, Issue 5
Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model

Rui Chen, Xiaofeng Yang & Hui Zhang

J. Comp. Math., 36 (2018), pp. 661-681.

Published online: 2018-06

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  • Abstract

In this paper, we present an efficient energy stable scheme to solve a phase field model incorporating contact line condition. Instead of the usually used Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field model with the static contact line boundary condition that coupled with incompressible Navier-Stokes equations with Navier boundary condition. The projection method is used to deal with the Navier-Stokes equations and an auxiliary function is introduced for the non-convex Ginzburg-Landau bulk potential. We show that the scheme is linear, decoupled and energy stable. Moreover, we prove that fully discrete scheme is also energy stable. An efficient finite element spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed scheme is very efficient and accurate.

  • Keywords

Moving contact line Phase-field Navier-Stokes equations Allen-Cahn equation Finite element Energy stable scheme Linear element

  • AMS Subject Headings

65N06 65B99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ruichenbnu@gmail.com (Rui Chen)

xfyang@math.sc.edu (Xiaofeng Yang)

hzhang@bnu.edu.cn (Hui Zhang)

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@Article{JCM-36-661, author = {Chen , Rui and Yang , Xiaofeng and Zhang , Hui }, title = {Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {5}, pages = {661--681}, abstract = {

In this paper, we present an efficient energy stable scheme to solve a phase field model incorporating contact line condition. Instead of the usually used Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field model with the static contact line boundary condition that coupled with incompressible Navier-Stokes equations with Navier boundary condition. The projection method is used to deal with the Navier-Stokes equations and an auxiliary function is introduced for the non-convex Ginzburg-Landau bulk potential. We show that the scheme is linear, decoupled and energy stable. Moreover, we prove that fully discrete scheme is also energy stable. An efficient finite element spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed scheme is very efficient and accurate.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1703-m2016-0614}, url = {http://global-sci.org/intro/article_detail/jcm/12451.html} }
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