A second‐order energy stable backward differentiation formula method for the epitaxial thin film equation with slope selection

W Feng, C Wang, SM Wise… - Numerical Methods for …, 2018 - Wiley Online Library
In this article, we study a new second‐order energy stable Backward Differentiation Formula
(BDF) finite difference scheme for the epitaxial thin film equation with slope selection (SS) …

[PDF][PDF] A general strategy for numerical approximations of non-equilibrium models-part I: thermodynamical systems

J Zhao, X Yang, Y Gong, X Zhao, X Yang… - Int. J. Numer. Anal …, 2018 - doc.global-sci.org
We present a general approach to deriving energy stable numerical approximations for
thermodynamical consistent models for nonequilibrium phenomena. The central idea …

Numerical comparison of modified-energy stable SAV-type schemes and classical BDF methods on benchmark problems for the functionalized Cahn-Hilliard equation

C Zhang, J Ouyang, C Wang, SM Wise - Journal of Computational Physics, 2020 - Elsevier
In this paper, we construct and test a class of linear numerical schemes for the
Functionalized Cahn-Hilliard (FCH) equation with a symmetric double-well potential function …

High accuracy solutions to energy gradient flows from material science models

A Christlieb, J Jones, K Promislow, B Wetton… - Journal of computational …, 2014 - Elsevier
A computational framework is presented for materials science models that come from energy
gradient flows. The models of interest lead to the evolution of structure involving two or more …

Second order fully discrete energy stable methods on staggered grids for hydrodynamic phase field models of binary viscous fluids

Y Gong, J Zhao, Q Wang - SIAM Journal on Scientific Computing, 2018 - SIAM
We present second order, fully discrete, energy stable methods on spatially staggered grids
for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry …

A uniquely solvable, energy stable numerical scheme for the functionalized Cahn–Hilliard equation and its convergence analysis

W Feng, Z Guan, J Lowengrub, C Wang… - Journal of Scientific …, 2018 - Springer
We present and analyze a uniquely solvable and unconditionally energy stable numerical
scheme for the Functionalized Cahn–Hilliard equation, including an analysis of …

Coarsening mechanism for systems governed by the Cahn--Hilliard equation with degenerate diffusion mobility

S Dai, Q Du - Multiscale Modeling & Simulation, 2014 - SIAM
We study a Cahn--Hilliard equation with a diffusion mobility that is degenerate in both
phases and a double-well potential that is continuously differentiable. Using asymptotic …

Geometric evolution of bilayers under the functionalized Cahn–Hilliard equation

S Dai, K Promislow - Proceedings of the Royal Society A …, 2013 - royalsocietypublishing.org
We use a multi-scale analysis to derive a sharp interface limit for the dynamics of bilayer
structures of the functionalized Cahn–Hilliard equation. In contrast to analysis based on …

Motion of interfaces governed by the Cahn--Hilliard equation with highly disparate diffusion mobility

S Dai, Q Du - SIAM Journal on Applied Mathematics, 2012 - SIAM
We consider a two-phase system governed by a Cahn--Hilliard type equation with a highly
disparate diffusion mobility. It has been observed from recent numerical simulations that the …

Meander and pearling of single-curvature bilayer interfaces in the functionalized Cahn--Hilliard equation

A Doelman, G Hayrapetyan, K Promislow… - SIAM Journal on …, 2014 - SIAM
The functionalized Cahn--Hilliard (FCH) free energy models interfacial energy in amphiphilic
phase separated mixtures. Its minimizers encompass a rich class of morphologies with …