# An efficient and energy stable scheme for a phase‐field model for the moving contact line problem

@article{Aland2016AnEA, title={An efficient and energy stable scheme for a phase‐field model for the moving contact line problem}, author={Sebastian Aland and Feng Chen}, journal={International Journal for Numerical Methods in Fluids}, year={2016}, volume={81}, pages={657-671} }

In this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier–Stokes– Cahn–Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing property of the discrete energy, and demonstrate the effectiveness of our method through numerical… Expand

#### 19 Citations

Efficient energy stable numerical schemes for a phase field moving contact line model

- Mathematics, Computer Science
- J. Comput. Phys.
- 2015

The efficiency and fast convergence of the proposed schemes with spectral spatial approximations are numerically verified andrete energy laws that are consistent to the continuous ones are proved. Expand

Fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities

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Abstract In this study, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model comprises a… Expand

Numerical approximations for a phase-field moving contact line model with variable densities and viscosities

- Mathematics, Physics
- J. Comput. Phys.
- 2017

This work considers the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line boundary conditions and develops two efficient, unconditionally energy stable numerical schemes. Expand

Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2018

We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn--Hilliard equation ...

Time integration for diffuse interface models for two-phase flow

- Mathematics, Computer Science
- J. Comput. Phys.
- 2014

We propose a variant of the @q-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional… Expand

A phase-field model for fluid-structure interaction

- Physics, Computer Science
- J. Comput. Phys.
- 2018

A novel phase-field model for fluid–structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to a wall, is developed. Expand

An unconditionally energy-stable scheme based on an implicit auxiliary energy variable for incompressible two-phase flows with different densities involving only precomputable coefficient matrices

- Physics, Mathematics
- J. Comput. Phys.
- 2019

An implication of this work is that energy-stable schemes for two-phase problems can also become computationally efficient and competitive, eliminating the need for expensive re-computations of coefficient matrices, even at large density ratios and viscosity ratios. Expand

Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

- Mathematics, Physics
- Journal of Fluid Mechanics
- 2018

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for binary fluids with moving contact lines are studied by asymptotic analysis and numerical… Expand

Comparison of energy stable simulation of moving contact line problems using a thermodynamically consistent Cahn-Hilliard Navier-Stokes model

- Physics, Mathematics
- J. Comput. Phys.
- 2019

The quality of the numerical results obtained are thoughtfully compared with three different schemes and two different bulk energy potentials and the influence of the different schemes on the apparent contact angles of a sliding droplet is discussed. Expand

Transient electrohydrodynamic flow with concentration-dependent fluid properties: Modelling and energy-stable numerical schemes

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- J. Comput. Phys.
- 2020

This work presents a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles, and proposes strategies for constructing numerical schemes for this set of equations, where the electrochemical and the hydrodynamic subproblems are decoupled at each time step. Expand

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Efficient energy stable numerical schemes for a phase field moving contact line model

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