相关论文: Convergence of substructuring Methods for the Cahn…

In this work we introduce the development of a three--phase incompressible Navier--Stokes/Cahn--Hilliard numerical method to simulate three--phase flows, present in many industrial operations. The numerical method is then applied to…

We consider coarsening dynamics associated with a Burgers--Cahn--Hilliard system modeling a two-phase flow in one space dimension. Our emphasis is on the effect that coupling between the phase and fluid dynamics has on coarsening rates, and…

In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…

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…

This paper proposes a method for rigorously analyzing the sign-change structure of solutions of elliptic partial differential equations subject to one of the three types of homogeneous boundary conditions: Dirichlet, Neumann, and mixed.…

The two-phase Navier-Stokes Cahn-Hilliard (NSCH) mixture model is a key framework for simulating multiphase flows with non-matching densities. Developing fully discrete, energy-stable schemes for this model remains challenging, due to the…

In this paper, we consider some hyperbolic variants of the mass conserving Allen-Cahn equation, which is a nonlocal reaction-diffusion equation, introduced (as a simpler alternative to the Cahn-Hilliard equation) to describe phase…

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…

We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn-Hilliard-Brinkman (CHB) system with a elliptic reaction-diffusion equation for a nutrient. The fluid velocity, governed by the Brinkman…

In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and…

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…

Non-overlapping domain decomposition methods necessarily have to exchange Dirichlet and Neumann traces at interfaces in order to be able to converge to the underlying mono-domain solution. Well known such non-overlapping methods are the…

A rigorous proof is given for the convergence of the solutions of a viscous Cahn-Hilliard system to the solution of the regularized version of the forward-backward parabolic equation, as the coefficient of the diffusive term goes to 0.…

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for…

In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward…

We study a quasi-incompressible Navier--Stokes/Cahn--Hilliard coupled system which describes the motion of two macroscopically immiscible incompressible viscous fluids with partial mixing in a small interfacial region and long-range…

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the…

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…

The first aim of this paper is to examine existence, uniqueness and regularity for the Cahn-Hilliard-Cook (CHC) equation in space dimension $d\leq 3$. By applying a spectral Galerkin method to the infinite dimensional equation, we elaborate…