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.
Highlights
The moving contact line problem, where the interface of the two immiscible fluids intersects the solid wall, has become one of the most interesting research topics in recent years
We have developed a three-dimensional adaptive finite element method for a phase field model for the moving contact line problem
Our method is based on a gradient stable semi-implicit scheme with mesh adaptation based on a posteriori error estimates
Summary
The moving contact line problem, where the interface of the two immiscible fluids intersects the solid wall, has become one of the most interesting research topics in recent years. Several numerical methods have been developed for the Cahn-Hilliard and NavierStokes system with the generalized Navied boundary condition [5, 6, 7]. Phase field, moving contact line, generalized Navier boundary condition, adaptive finite element. To simulate this different behavior of the solutions efficiently, a multi-mesh adaptive finite element method was developed in [5], which approximates different components of the solution (velocity, pressure and phase variable) on different h-adaptive meshes.
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