An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model

DOI10.4208/aamm.OA-2020-0044zbMath1488.65489OpenAlexW3152492915MaRDI QIDQ5157066

Haiyan Su, Jianping Zhao, Rui Chen

Publication date: 12 October 2021

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/aamm.oa-2020-0044

zbMATH Keywords

finite element methodCahn-Hilliard equationmagnetohydrodynamic equationsabsolutely energy-stableconstant auxiliary variable

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Magnetohydrodynamics and electrohydrodynamics (76W05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Liquid-liquid two component flows (76T06)

Related Items (6)

Unconditional stability and optimal error estimates of first order semi-implicit stabilized finite element method for two phase magnetohydrodynamic diffuse interface model ⋮ Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn-Hilliard-magnetohydrodynamics system of equations ⋮ Gauge-Uzawa-based, highly efficient decoupled schemes for the diffuse interface model of two-phase magnetohydrodynamic ⋮ Decoupled, linear, unconditionally energy stable and charge-conservative finite element method for an inductionless magnetohydrodynamic phase-field model ⋮ Energy stable schemes with second order temporal accuracy and decoupled structure for diffuse interface model of two-phase magnetohydrodynamics ⋮ A Finite Element Variational Multiscale Method for Stationary Incompressible Magnetohydrodynamics Equations

Uses Software

• FEAPpv

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform \(H^{2}\)-regularity of solution for the 2D Navier-Stokes/Cahn-Hilliard phase field model
• Stability and uniqueness in double porosity elasticity
• A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system
• A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D
• On anisotropic order parameter models for multi-phase systems and their sharp interface limits
• A semi-implicit energy conserving finite element method for the dynamical incompressible magnetohydrodynamics equations
• A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows
• Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows
• The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab
• Two-level Newton iterative method for the 2D/3D stationary incompressible magnetohydrodynamics
• Two-level penalty Newton iterative method for the 2D/3D stationary incompressible magnetohydrodynamics equations
• Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows
• A theory of hyperelasticity of multi-phase media with surface/interface energy effect
• Error Analysis of a Mixed Finite Element Method for the Molecular Beam Epitaxy Model
• On the Existence, Uniqueness, and Finite Element Approximation of Solutions of the Equations of Stationary, Incompressible Magnetohydrodynamics
• Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
• Fully Discrete Finite Element Approximations of the Navier--Stokes--Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid Flows
• Numerical analysis of the Crank–Nicolson extrapolation time discrete scheme for magnetohydrodynamics flows
• Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration
• Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
• Compact difference schemes for heat equation with Neumann boundary conditions
• Two-Level Method Based on Finite Element and Crank-Nicolson Extrapolation for the Time-Dependent Navier-Stokes Equations
• The Hermite Spectral Method for Gaussian-Type Functions
• Finite Element Methods for Maxwell's Equations
• On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes
• TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER
• On a Large Time-Stepping Method for the Swift-Hohenberg Equation
• The Oseen Type Finite Element Iterative Method for the Stationary Incompressible Magnetohydrodynamics
• A Convex-Splitting Scheme for a Diffuse Interface Model with Peng-Robinson Equation of State
• Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models

This page was built for publication: An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model