A second‐order energy stable backward differentiation formula method for the epitaxial thin film equation with slope selection
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) …
(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
We present a general approach to deriving energy stable numerical approximations for
thermodynamical consistent models for nonequilibrium phenomena. The central idea …
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
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 …
Functionalized Cahn-Hilliard (FCH) equation with a symmetric double-well potential function …
High accuracy solutions to energy gradient flows from material science models
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 …
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
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 …
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
We present and analyze a uniquely solvable and unconditionally energy stable numerical
scheme for the Functionalized Cahn–Hilliard equation, including an analysis of …
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
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 …
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 …
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
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 …
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 …
phase separated mixtures. Its minimizers encompass a rich class of morphologies with …