A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space

DOI10.4208/cicp.OA-2018-0202zbMath1486.65107MaRDI QIDQ5162007

Yibao Li, Junseok Kim, Darae Jeong, Chaeyoung Lee, Junxiang Yang

Publication date: 1 November 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

zbMATH Keywords

Cahn-Hilliard equationclosest point methodnarrow band domainmass correction scheme

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (9)

Efficient and practical phase-field method for the incompressible multi-component fluids on 3D surfaces with arbitrary shapes ⋮ An explicit adaptive finite difference method for the Cahn-Hilliard equation ⋮ A simple and practical finite difference method for the phase-field crystal model with a strong nonlinear vacancy potential on 3D surfaces ⋮ Surface phase-field surfactant fluid model and its practical closest point type finite difference computation ⋮ Linear and conservative IMEX Runge-Kutta finite difference schemes with provable energy stability for the Cahn-Hilliard model in arbitrary domains ⋮ A conservative finite difference scheme for the \(N\)-component Cahn-Hilliard system on curved surfaces in 3D ⋮ A phase-field model and its efficient numerical method for two-phase flows on arbitrarily curved surfaces in 3D space ⋮ Phase-field computations of anisotropic ice crystal growth on a spherical surface ⋮ Phase field modeling and computation of multi-component droplet evaporation

Cites Work

• A benchmark for the surface Cahn-Hilliard equation
• Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition
• Level set equations on surfaces via the closest point method
• Solving eigenvalue problems on curved surfaces using the closest point method
• Finite element approximation of the Cahn-Hilliard equation on surfaces
• Motion by mean curvature of curves on surfaces using the Allen-Cahn Equation
• Direct discretization method for the Cahn-Hilliard equation on an evolving surface
• Basic principles and practical applications of the Cahn-Hilliard equation
• Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
• An unconditionally energy-stable second-order time-accurate scheme for the Cahn-Hilliard equation on surfaces
• A phase-field fluid modeling and computation with interfacial profile correction term
• Multi-component Cahn-Hilliard system with different boundary conditions in complex domains
• Fourth order partial differential equations on general geometries
• Inpainting of Binary Images Using the Cahn–Hilliard Equation
• On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn–Hilliard Functional
• Numerical Studies of the Cahn-Hilliard Equation for Phase Separation
• Phase-Field Models for Multi-Component Fluid Flows
• On the Cahn–Hilliard Equation with Degenerate Mobility
• Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model
• Topology Optimization of Capillary, Two-Phase Flow Problems
• A Flux-Corrected Phase-Field Method for Surface Diffusion
• A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation
• Preconditioning of a Coupled Cahn-Hilliard Navier-Stokes System
• Free Energy of a Nonuniform System. I. Interfacial Free Energy

This page was built for publication: A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space