相关论文: An Energy Stable Finite-Difference Scheme for Func…
In this paper, we consider the numerical approximations for the fourth order Cahn-Hilliard equation with concentration dependent mobility, and the logarithmic Flory-Huggins potential. One challenge in solving such a diffusive system…
We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier- Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection…
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 consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between…
The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
We propose a novel decoupled unconditionally stable numerical scheme for the simulation of two-phase flow in a Hele-Shaw cell which is governed by the Cahn-Hilliard-Hele-Shaw system (CHHS) with variable viscosity. The temporal…
In this paper, we provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, which follows from consistency and stability estimates for the numerical…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
In this paper, we consider numerical approximations for the anisotropic Cahn-Hilliard equation. The main challenge of constructing numerical schemes with unconditional energy stabilities for this model is how to design proper temporal…
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which…
In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy for solving both the Cahn-Hilliard equation and the Allen-Cahn…
In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different…
We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…
We present a numerical scheme for solving a sixth-order Cahn-Hilliard type equation that captures the dynamics of phase transitions in a ternary mixture consisting of two immiscible fluids and a surface active molecule that is amphiphilic.…
Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algorithm for solving the Cahn-Hilliard-Navier-Stokes equations within a decoupled splitting framework. We show that the proposed scheme is uniquely solvable…
The space fractional Cahn-Hilliard phase-field model is more adequate and accurate in the description of the formation and phase change mechanism than the classical Cahn-Hilliard model. In this article, we propose a temporal second-order…
We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary…