Journal ArticleDOI
A numerical method for the ternary Cahn--Hilliard system with a degenerate mobility
Junseok Kim,Kyungkeun Kang +1 more
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TLDR
This work applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a Ternary mixture and proved stability of the numerical solution for a sufficiently small time step.About:
This article is published in Applied Numerical Mathematics.The article was published on 2009-05-01. It has received 24 citations till now. The article focuses on the topics: Numerical stability & Multigrid method.read more
Citations
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Journal ArticleDOI
Phase-Field Models for Multi-Component Fluid Flows
TL;DR: In this article, the authors review the recent development of phase-field models and their numerical methods for multi-component fluid flows with interfacial phenomena, and provide practical applications to illustrate the usefulness of using a phasefield method.
Journal ArticleDOI
The Cahn-Hilliard Equation with Logarithmic Potentials
TL;DR: In this paper, the authors discuss recent issues related with the Cahn-Hilliard equation in phase separation with the thermodynamically relevant logarithmic potentials; in particular, they are interested in the wellposedness and the study of the asymptotic behavior of the solutions (and more precisely the existence of finite-dimensional attractors).
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Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem
TL;DR: It is demonstrated that significant computational gains can be obtained by applying embedded, higher order Runge-Kutta methods in a time adaptive setting, which allows accessing time-scales that vary by five orders of magnitude.
Journal ArticleDOI
The Cahn–Hilliard equation and some of its variants
TL;DR: In this article, the authors review and discuss the Cahn-Hilliard equation, as well as its variants, and some of its variants have applications in biology and image inpainting.
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A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system
TL;DR: The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method and allows the N-component Cahn–Hilliard system to be converted into a system of N−1 binary Cahn-Hilliard equations and significantly reduces the required computer memory and CPU time.
References
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Book
Phase transformations in metals and alloys
TL;DR: In this article, the authors discuss the properties of phase diagrams for single-component systems, including the influence of interfaces on the equilibrium of binary solutions in Heterogeneous Systems (Heterogeneous Binary Phase Diagrams).
Book ChapterDOI
The Cahn-Hilliard Model for the Kinetics of Phase Separation
TL;DR: In this paper, the Cahn-Hilliard mathematical continuum model of spinodal decomposition (or phase separation) of a binary alloy is considered and the phenomenological model is derived.
Journal ArticleDOI
A second order splitting method for the Cahn-Hilliard equation
TL;DR: In this paper, a semi-discrete finite element method requiring only continuous element is presented for the approximation of the solution of the evolutionary, fourth order in space, Cahn-Hilliard equation.
Journal ArticleDOI
A stable and conservative finite difference scheme for the Cahn-Hilliard equation
TL;DR: A stable and conservative finite difference scheme to solve numerically the Cahn-Hilliard equation which describes a phase separation phenomenon and inherits characteristic properties, the conservation of mass and the decrease of the total energy, from the equation.
Journal ArticleDOI
Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation
Charles M. Elliott,Stig Larsson +1 more
TL;DR: In this article, a finite element method for the Cahn-Hilliard equation (a semilinear parabolic equation of fourth order) is analyzed, both in a spatially semidiscrete case and in a completely discrete case based on the backward Euler method.