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

Yu, Haijun; Yang, Xiaofeng

doi:10.1016/j.jcp.2017.01.026

Cited by 76 publications

(58 citation statements)

References 70 publications

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“…It is a common approach to cut ϕ when inserting it into the linear function for ρ, see e.g. [18]. This leads to a nonsmooth relation between ϕ and ρ.…”

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 99%

“…In both cases we can decouple the Navier-Stokes equation and the Cahn-Hilliard equation by using an augmented velocity field in (18), see for example [11,13,18,37]. Here we substitute −…”

Section: A Stable Decoupled Schemementioning

confidence: 99%

“…Here the concepts from the aforementioned papers for the discretization of the bulk equations are straightforwardly applied. For the case of equal densities, schemes are proposed, e.g., in [14][15][16][17] and for the case of different densities in [11,18]. The model from [8] contains an additional flux term in the momentum equation, that renders the model thermodynamically consistent.…”

Section: Introductionmentioning

confidence: 99%

“…This term is often neglected, see e.g., [19]. For the resulting model several discretization schemes are proposed and we refer to the references in [18] for details. In all these simulations involving moving contact lines a polynomial bulk energy potential is applied.…”

Section: Introductionmentioning

confidence: 99%

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

Bonart

Kahle

Repke

2019

Journal of Computational Physics

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Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. To model this situation, we use a phase field approach. The bulk model is given by the thermodynamically consistent Cahn-Hilliard Navier-Stokes model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22 (3), 2012]. To model the contact line dynamics we apply the generalized Navier boundary condition for the fluid and the dynamically advected boundary contact angle condition for the phase field as derived in [Qian et al., J. Fluid Mech., 564, 2006]. In recent years several schemes were proposed to solve this model numerically. While they widely differ in terms of complexity, they all fulfill certain basic properties when it comes to thermodynamic consistency. However, an accurate comparison of the influence of the schemes on the moving contact line is rarely found. Therefore, we thoughtfully compare the quality of the numerical results obtained with three different schemes and two different bulk energy potentials. Especially, we discuss the influence of the different schemes on the apparent contact angles of a sliding droplet.

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“…It is a common approach to cut ϕ when inserting it into the linear function for ρ, see e.g. [18]. This leads to a nonsmooth relation between ϕ and ρ.…”

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 99%

“…In both cases we can decouple the Navier-Stokes equation and the Cahn-Hilliard equation by using an augmented velocity field in (18), see for example [11,13,18,37]. Here we substitute −…”

Section: A Stable Decoupled Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Bonart

Kahle

Repke

2019

Journal of Computational Physics

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“…We start with convergence test using Couette flow with different density and viscosity [47,49] as in Fig. 2.…”

Section: Convergence Study: Couette Flowmentioning

confidence: 99%

An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

Shen

Huang

Lin

et al. 2020

Journal of Computational Physics

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In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with General Navier Boundary Condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.

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A novel fully decoupled scheme with second‐order time accuracy and unconditional energy stability for the Navier‐Stokes equations coupled with mass‐conserved Allen‐Cahn phase‐field model of two‐phase incompressible flow

Yang

2020

Int J Numer Methods Eng

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We consider the numerical approximation of the flow-coupled phase-field model of two-phase incompressible flows using the mass-conserved Allen-Cahn equation. Due to the highly nonlinear nature of the coupling, how to develop an accurate and practically efficient scheme has always been a challenging problem. To solve this challenge, we construct a novel effective fully decoupled scheme that is linear, unconditional energy stable, and second-order time accurate. The key idea of decoupling is to introduce a nonlocal variable and a related ordinary differential equation to deal with the nonlinear coupling terms that satisfy the so-called "zero-energy-contribution" property. Thus, in actual calculations, this scheme only needs to solve several independent linear equations at each time step to obtain a numerical solution with the second-order time accuracy. We strictly prove the solvability and unconditional energy stability and perform numerical simulations in 2D and 3D to verify the accuracy and stability of the scheme numerically.

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

Cited by 76 publications

References 70 publications

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

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

An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

A novel fully decoupled scheme with second‐order time accuracy and unconditional energy stability for the Navier‐Stokes equations coupled with mass‐conserved Allen‐Cahn phase‐field model of two‐phase incompressible flow

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