3D adaptive finite element method for a phase field model for the moving contact line problems

Yi Shi; Kai Bao; Xiao-Ping Wang

doi:10.3934/ipi.2013.7.947

Article Contents

2013, Volume 7, Issue 3: 947-959. Doi: 10.3934/ipi.2013.7.947

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3D adaptive finite element method for a phase field model for the moving contact line problems

1.
Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
2.
Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia
3.
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received: June 30, 2012

Revised: November 30, 2012

Published: July 2013

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Abstract

In this paper, we propose an adaptive finite element method for simulating the moving contact line problems in three dimensions. The model that we used is the coupled Cahn-Hilliard Navier-Stokes equations with the generalized Navier boundary condition(GNBC) proposed in [18]. In our algorithm, to improve the efficiency of the simulation, we use the residual type adaptive finite element algorithm. It is well known that the phase variable decays much faster away from the interface than the velocity variables. Therefore we use an adaptive strategy that will take into account of such difference. Numerical experiments show that our algorithm is both efficient and reliable.

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Mathematics Subject Classification: Primary: 74S05; Secondary: 76D45.

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