A fully-discrete decoupled finite element method for the conserved Allen-Cahn type phase-field model of three-phase fluid flow system

DOI10.1016/j.cma.2021.114376OpenAlexW3215555820MaRDI QIDQ2072475

Xiaoming He, Xiao-Feng Yang

Publication date: 26 January 2022

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2021.114376

zbMATH Keywords

finite element methodunconditional stabilityfully discrete schemephase fieldthree-phase flowsconserved Allen-Cahn model

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10) Three or more component flows (76T30)

Related Items (20)

A novel second-order time accurate fully discrete finite element scheme with decoupling structure for the hydrodynamically-coupled phase field crystal model ⋮ Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities ⋮ Unconditionally energy-stable time-marching methods for the multi-phase conservative Allen-Cahn fluid models based on a modified SAV approach ⋮ Optimal rate convergence analysis of a numerical scheme for the ternary Cahn-Hilliard system with a Flory-Huggins-deGennes energy potential ⋮ Numerical approximations of flow coupled binary phase field crystal system: fully discrete finite element scheme with second-order temporal accuracy and decoupling structure ⋮ Comparing the convected level-set and the Allen-Cahn phase-field methods in AMR/C simulations of two-phase flows ⋮ A decoupled and iterative finite element method for generalized Boussinesq equations ⋮ A fully decoupled numerical method for Cahn-Hilliard-Navier-Stokes-Darcy equations based on auxiliary variable approaches ⋮ Thermodynamically consistent hydrodynamic phase-field computational modeling for fluid-structure interaction with moving contact lines ⋮ Fully discrete, decoupled and energy-stable Fourier-spectral numerical scheme for the nonlocal Cahn-Hilliard equation coupled with Navier-Stokes/Darcy flow regime of two-phase incompressible flows ⋮ Reformulated Weak Formulation and Efficient Fully Discrete Finite Element Method for a Two-Phase Ferrohydrodynamics Shliomis Model ⋮ Linearly implicit and high-order energy-preserving relaxation schemes for highly oscillatory Hamiltonian systems ⋮ A thermodynamically consistent diffuse interface model for the wetting phenomenon of miscible and immiscible ternary fluids ⋮ Linear energy-stable method with correction technique for the Ohta-Kawasaki-Navier-Stokes model of incompressible diblock copolymer melt ⋮ Unnamed Item ⋮ Fully-discrete Spectral-Galerkin scheme with second-order time-accuracy and unconditionally energy stability for the volume-conserved phase-field lipid vesicle model ⋮ Decoupled, second-order accurate in time and unconditionally energy stable scheme for a hydrodynamically coupled ternary Cahn-Hilliard phase-field model of triblock copolymer melts ⋮ Efficient linear, fully-decoupled and energy stable numerical scheme for a variable density and viscosity, volume-conserved, hydrodynamically coupled phase-field elastic bending energy model of lipid vesicles ⋮ Fully-discrete spectral-Galerkin numerical scheme with second-order time accuracy and unconditional energy stability for the anisotropic Cahn-Hilliard model ⋮ Fully discrete spectral-Galerkin scheme for a ternary Allen-Cahn type mass-conserved Nakazawa-Ohta phase-field model for triblock copolymers

Cites Work

• Unnamed Item
• An unconditionally energy-stable method for the phase field crystal equation
• Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation
• A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation
• A conservative phase field method for solving incompressible two-phase flows
• Mass conserving Allen-Cahn equation and volume preserving mean curvature flow
• Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
• Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry
• Energy stable numerical schemes for ternary Cahn-Hilliard system
• Conservative multigrid methods for ternary Cahn-Hilliard systems
• Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation
• Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method
• Gauge-Uzawa methods for incompressible flows with variable density
• Finite element approximation of a Cahn-Hilliard-Navier-Stokes system
• A splitting method for incompressible flows with variable density based on a pressure Poisson equation
• A conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier
• A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system
• Numerical approximations for a smectic-A liquid crystal flow model: first-order, linear, decoupled and energy stable schemes
• A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows
• Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method
• Conservative Allen-Cahn-Navier-Stokes system for incompressible two-phase fluid flows
• Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
• Convergence analysis and error estimates for a second order accurate finite element method for the Cahn-Hilliard-Navier-Stokes system
• Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
• Multiphase Allen-Cahn and Cahn-Hilliard models and their discretizations with the effect of pairwise surface tensions
• The scalar auxiliary variable (SAV) approach for gradient flows
• An adaptive variational procedure for the conservative and positivity preserving Allen-Cahn phase-field model
• A stochastic mass conserved reaction-diffusion equation with nonlinear diffusion
• Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model
• Efficient and accurate numerical scheme for a magnetic-coupled phase-field-crystal model for ferromagnetic solid materials
• A new efficient fully-decoupled and second-order time-accurate scheme for Cahn-Hilliard phase-field model of three-phase incompressible flow
• Existence and weak-strong uniqueness of solutions to the Cahn-Hilliard-Navier-Stokes-Darcy system in superposed free flow and porous media
• Efficient and energy stable scheme for the hydrodynamically coupled three components Cahn-Hilliard phase-field model using the stabilized-invariant energy quadratization (S-IEQ) approach
• Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard model
• A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows
• Unconditionally energy stable large time stepping method for the \(L^2\)-gradient flow based ternary phase-field model with precise nonlocal volume conservation
• Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields
• Efficient numerical scheme for a dendritic solidification phase field model with melt convection
• 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
• Decoupled, non-iterative, and unconditionally energy stable large time stepping method for the three-phase Cahn-Hilliard phase-field model
• Numerical approximations for the hydrodynamics coupled binary surfactant phase field model: second-order, linear, unconditionally energy-stable schemes
• On efficient numerical schemes for a two-mode phase field crystal model with face-centered-cubic (FCC) ordering structure
• Fast, unconditionally energy stable large time stepping method for a new Allen-Cahn type square phase-field crystal model
• A diffuse interface model for two-phase ferrofluid flows
• Numerical analysis of second order, fully discrete energy stable schemes for phase field models of two-phase incompressible flows
• Phase field modeling and simulation of three-phase flows
• An overview of projection methods for incompressible flows
• Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density
• Numerical approximations for a new \(L^2\)-gradient flow based phase field crystal model with precise nonlocal mass conservation
• Analysis of Mixed Interior Penalty Discontinuous Galerkin Methods for the Cahn–Hilliard Equation and the Hele–Shaw Flow
• Numerical schemes for a three component Cahn-Hilliard model
• A DIFFUSE INTERFACE MODEL FOR ELECTROWETTING WITH MOVING CONTACT LINES
• Analysis of a Darcy--Cahn--Hilliard Diffuse Interface Model for the Hele-Shaw Flow and Its Fully Discrete Finite Element Approximation
• Analysis of a Mixed Finite Element Method for a Cahn--Hilliard--Darcy--Stokes System
• Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows
• Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density
• An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
• A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities
• Study of a three component Cahn-Hilliard flow model
• Analysis of finite element approximations of a phase field model for two-phase fluids
• Fully Discrete Finite Element Approximations of the Navier--Stokes--Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid Flows
• Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen–Cahn equation and the mean curvature flow
• An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
• A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow
• Nonlocal reaction—diffusion equations and nucleation
• Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach
• Decoupled, Linear, and Energy Stable Finite Element Method for the Cahn--Hilliard--Navier--Stokes--Darcy Phase Field Model
• Projection Method I: Convergence and Numerical Boundary Layers
• On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes
• An unconditionally stable uncoupled scheme for a triphasic Cahn–Hilliard/Navier–Stokes model
• The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems
• A positivity-preserving and convergent numerical scheme for the binary fluid-surfactant system
• An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation
• Efficient, second-order in time, and energy stable scheme for a new hydrodynamically coupled three components volume-conserved Allen–Cahn phase-field model
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
• A new linearly extrapolated Crank-Nicolson time-stepping scheme for the Navier-Stokes equations
• Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
• Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids
• The Gauge--Uzawa Finite Element Method. Part I: The Navier--Stokes Equations
• Motion of a Droplet for the Stochastic Mass-Conserving Allen--Cahn Equation
• Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
• Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model
• A projection FEM for variable-density incompressible flows

This page was built for publication: A fully-discrete decoupled finite element method for the conserved Allen-Cahn type phase-field model of three-phase fluid flow system