An energy stable $C^0$ finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

Abstract

In this paper, we focus on modeling and simulation of two-phase flow 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. Then a mass conserving and energy stable C0 finite element scheme is developed to solve the PDE system. Various numerical simulation results show that the proposed schemes are mass conservative, energy stable and the 2nd order for P1 element and 3rd order for P2 element convergence rate in the sense of L2 norm.

References in corpus (12)

• Two-phase binary fluids and immiscible fluids described by an order parameter
• A variational approach to the moving contact line hydrodynamics
• A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects
• A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law
• Numerical Approximations for a Phase-Field Moving Contact Line Model with Variable Densities and Viscosities
• Efficient Second Order Unconditionally Stable Schemes for a Phase-field Moving Contact Line Model Using Invariant Energy Quadratization Approach
• Mass Conservative and Energy Stable Finite Difference Methods for the Quasi-incompressible Navier-Stokes-Cahn-Hilliard system: Primitive Variable and Projection-Type Schemes
• Arbitrarily High-order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
• An Energetic Variational Approach for ion transport
• Moving Contact Lines: Linking Molecular Dynamics and Continuum-Scale Modeling
• Osmosis through a Semi-permeable Membrane: a Consistent Approach to Interactions
• Thermodynamically Consistent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities

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• A phase field model for mass transport with semi-permeable interfaces
• Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows