A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations

DOI10.4208/aamm.OA-2020-0293zbMath1499.65389OpenAlexW3215234921WikidataQ114021265 ScholiaQ114021265MaRDI QIDQ5032342

Tongmao Li, Xiao-Feng Yang, Qiongwei Ye, Shuang Geng

Publication date: 16 February 2022

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-2020-0293

zbMATH Keywords

second orderphase-fieldnonlocalAllen-Cahnunconditional energy stabilitydiblock copolymer

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Statistical mechanics of polymers (82D60) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (7)

A new Allen-Cahn type two-model phase-field crystal model for fcc ordering and its numerical approximation ⋮ Maximum principle preserving and unconditionally stable scheme for a conservative Allen-Cahn equation ⋮ Stability analysis for a maximum principle preserving explicit scheme of the Allen-Cahn equation ⋮ Large time-stepping, delay-free, and invariant-set-preserving integrators for the viscous Cahn-Hilliard-Oono equation ⋮ 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 ⋮ A phase-field method for elastic mechanics with large deformation ⋮ Fully discrete spectral-Galerkin scheme for a ternary Allen-Cahn type mass-conserved Nakazawa-Ohta phase-field model for triblock copolymers

Cites Work

• A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver
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• Decoupled, non-iterative, and unconditionally energy stable large time stepping method for the three-phase Cahn-Hilliard phase-field model
• Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations
• Dynamics of fluctuations and spinodal decomposition in polymer blends
• Nonlocal reaction—diffusion equations and nucleation
• Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model
• Decoupled, Linear, and Energy Stable Finite Element Method for the Cahn--Hilliard--Navier--Stokes--Darcy Phase Field Model
• The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems

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