Discontinuous Galerkin finite element method applied to the coupled unsteady Stokes/Cahn‐Hilliard equations
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DOI: 10.1002/fld.4720
Abstract: Two-phase flows driven by the interfacial dynamics are studied by tracking implicitly interfaces in the framework of the Cahn-Hilliard theory. The fluid dynamics is described by the Stokes equations with an additional source term in… read more here.
Keywords: finite element; discontinuous galerkin; galerkin finite; equation ... See more keywords
Slow dynamics for the hyperbolic Cahn‐Hilliard equation in one‐space dimension
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DOI: 10.1002/mma.5525
Abstract: The aim of this paper is to study the metastable properties of the solutions to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one space dimension, subject to either Neumann or Dirichlet boundary conditions.… read more here.
Keywords: space dimension; equation one; one space; hilliard equation ... See more keywords
On a Cahn‐Hilliard model for image segmentation
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DOI: 10.1002/mma.7146
Abstract: Our aim in this paper is to study the existence and uniqueness of solutions to a Cahn‐Hilliard type model proposed for image segmentation. We also prove the existence of unbounded (as time goes to infinity)… read more here.
Keywords: hilliard model; cahn hilliard; image segmentation;
Sharp limit of the viscous Cahn–Hilliard equation and thermodynamic consistency
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DOI: 10.1007/s00161-015-0434-5
Abstract: Diffuse and sharp interface models represent two alternatives to describe phase transitions with an interface between two coexisting phases. The two model classes can be independently formulated. Thus there arises the problem whether the sharp… read more here.
Keywords: diffuse; viscous cahn; model; sharp limit ... See more keywords
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems
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DOI: 10.1007/s00161-021-01045-9
Abstract: At high temperature and pressure, solid diffusion and chemical reactions between rock minerals lead to phase transformations. Chemical transport during uphill diffusion causes phase separation, that is, spinodal decomposition. Thus, to describe the coarsening kinetics… read more here.
Keywords: cahn framework; cahn; larch cahn; cahn hilliard ... See more keywords
Nonlocal-to-Local Convergence of Cahn–Hilliard Equations: Neumann Boundary Conditions and Viscosity Terms
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DOI: 10.1007/s00205-020-01573-9
Abstract: We consider a class of nonlocal viscous Cahn–Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential is allowed to be singular (e.g. of logarithmic type), while the singularity of the convolution kernel… read more here.
Keywords: boundary conditions; hilliard equations; neumann boundary; cahn hilliard ... See more keywords
Uniquely solvable and energy stable decoupled numerical schemes for the Cahn–Hilliard–Stokes–Darcy system for two-phase flows in karstic geometry
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DOI: 10.1007/s00211-017-0870-1
Abstract: We propose and analyze two novel decoupled numerical schemes for solving the Cahn–Hilliard–Stokes–Darcy (CHSD) model for two-phase flows in karstic geometry. In the first numerical scheme, we explore a fractional step method (operator splitting) to… read more here.
Keywords: system; decoupled numerical; numerical schemes; geometry ... See more keywords
An error estimate for a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions
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DOI: 10.1007/s00211-021-01230-7
Abstract: In the paper we consider a finite-volume approximation for the Cahn-Hilliard equation with dynamic boundary conditions. We prove an error estimate for the fully-discrete scheme. We also give numerical simulations which validate the theoretical result. read more here.
Keywords: boundary conditions; finite volume; dynamic boundary; equation dynamic ... See more keywords
Weak Solutions to the Cahn-Hilliard Equation with Degenerate Diffusion Mobility in ℝN
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DOI: 10.1007/s10114-019-8318-4
Abstract: This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonlinear… read more here.
Keywords: hilliard equation; cahn hilliard; equation degenerate; mobility ... See more keywords
Image Segmentation Using the Cahn–Hilliard Equation
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DOI: 10.1007/s10915-018-00899-7
Abstract: In this paper, we propose a novel model for image segmentation by using the Cahn–Hilliard equation. An interesting feature of this model lies in its ability of interpolating missing contours along wide gaps in order… read more here.
Keywords: using cahn; segmentation using; segmentation; image segmentation ... See more keywords
A Second Order in Time, Decoupled, Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Darcy System
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DOI: 10.1007/s10915-018-0748-0
Abstract: We propose a novel second order in time, fully decoupled and unconditionally stable numerical scheme for solving the Cahn–Hilliard–Darcy system which models two-phase flow in porous medium or in a Hele–Shaw cell. The scheme is… read more here.
Keywords: order; second order; darcy; order time ... See more keywords