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

Rui Chen, Xiaofeng Yang & Hui Zhang

DOI: 10.4208/jcm.1703-m2016-0614

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)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-661, author = {Chen , RuiYang , 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} }
TY - JOUR T1 - Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model AU - Chen , Rui AU - Yang , Xiaofeng AU - Zhang , Hui JO - Journal of Computational Mathematics VL - 5 SP - 661 EP - 681 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1703-m2016-0614 UR - https://global-sci.org/intro/article_detail/jcm/12451.html KW - Moving contact line, Phase-field, Navier-Stokes equations, Allen-Cahn equation, Finite element, Energy stable scheme, Linear element. AB -

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.

Chen , RuiYang , Xiaofeng and Zhang , Hui. (2018). Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model. Journal of Computational Mathematics. 36 (5). 661-681. doi:10.4208/jcm.1703-m2016-0614
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