Related papers: Cahn-Hilliard on Surfaces: A Numerical Study
In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for…
In this paper, we analyze a substructuring type algorithm for the Cahn-Hilliard (CH) equation. Being a nonlinear equation, it is of great importance to develop efficient numerical schemes for investigating the solution behaviour of the CH…
In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion type dynamics is derived on the basis…
In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of…
We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…
We consider a diffuse interface model that describes the macro- and micro-phase separation processes of a polymer mixture. The resulting system consists of a Cahn-Hilliard equation and a Cahn-Hilliard-Oono type equation endowed with the…
The Navier-Stokes-Cahn-Hilliard (NSCH) system governs the diffuse-interface dynamics of two incompressible and immiscible fluids. We consider a relaxation approximation of the NSCH system that is composed by a system of first-order…
We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish optimal order error bounds for a (fully…
We construct a decoupled, first-order, fully discrete, and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme is divided into two main parts. The first part involves the calculation of the…
We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete…
This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable…
In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective Cahn-Hilliard system,…
In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock…
In this paper we propose and analyze an energy stable numerical scheme for the Cahn-Hilliard equation, with second order accuracy in time and the fourth order finite difference approximation in space. In particular, the truncation error for…
We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…
A computationally efficient, low order finite element formulation is developed for modelling the Navier-Stokes-Cahn-Hilliard equations, which have been established as a promising phase field modelling approach for simulation of immiscible…
The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss…
The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermodynamics with flow. This review surveys the thermodynamic…
We construct rigorously suitable approximate solutions to the Stokes/Cahn-Hilliard system by using the method of matched asymptotics expansions. This is a main step in the proof of convergence given in the first part of this contribution,…
We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a…