The phase field method for geometric moving interfaces and their numerical approximations

Q Du, X Feng - Handbook of numerical analysis, 2020 - Elsevier
This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

Basic principles and practical applications of the Cahn–Hilliard equation

J Kim, S Lee, Y Choi, SM Lee… - … Problems in Engineering, 2016 - Wiley Online Library
The celebrated Cahn–Hilliard (CH) equation was proposed to model the process of phase
separation in binary alloys by Cahn and Hilliard. Since then the equation has been …

A novel fully-decoupled, second-order and energy stable numerical scheme of the conserved Allen–Cahn type flow-coupled binary surfactant model

X Yang - Computer Methods in Applied Mechanics and …, 2021 - Elsevier
In this paper, we establish a binary fluid surfactant model by coupling two mass-conserved
Allen–Cahn equations and the Navier–Stokes equations and consider numerical …

Wetting resistance at its topographical limit: the benefit of mushroom and serif T structures

R Hensel, R Helbig, S Aland, HG Braun, A Voigt… - Langmuir, 2013 - ACS Publications
Springtails (Collembola) are wingless arthropods adapted to cutaneous respiration in
temporarily rain-flooded habitats. They immediately form a plastron, protecting them against …

A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn–Hilliard–Navier–Stokes equation

D Han, X Wang - Journal of Computational Physics, 2015 - Elsevier
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 …

Convergence analysis and error estimates for a second order accurate finite element method for the Cahn–Hilliard–Navier–Stokes system

AE Diegel, C Wang, X Wang, SM Wise - Numerische Mathematik, 2017 - Springer
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 …

On linear schemes for a Cahn–Hilliard diffuse interface model

F Guillén-González, G Tierra - Journal of Computational Physics, 2013 - Elsevier
Numerical schemes to approximate the Cahn–Hilliard equation have been widely studied in
recent times due to its connection with many physically motivated problems. In this work we …

A second order BDF numerical scheme with variable steps for the Cahn--Hilliard equation

W Chen, X Wang, Y Yan, Z Zhang - SIAM Journal on Numerical Analysis, 2019 - SIAM
We present and analyze a second order in time variable step BDF2 numerical scheme for
the Cahn--Hilliard equation. The construction relies on a second order backward difference …

A novel fully decoupled scheme with second‐order time accuracy and unconditional energy stability for the Navier‐Stokes equations coupled with mass‐conserved …

X Yang - International Journal for Numerical Methods in …, 2021 - Wiley Online Library
We consider the numerical approximation of the flow‐coupled phase‐field model of two‐
phase incompressible flows using the mass‐conserved Allen‐Cahn equation. Due to the …

Asymptotic behavior of a Cahn–Hilliard–Navier–Stokes system in 2D

CG Gal, M Grasselli - Annales de l'IHP Analyse non linéaire, 2010 - numdam.org
We consider a model for the flow of a mixture of two homogeneous and incompressible
fluids in a two-dimensional bounded domain. The model consists of a Navier–Stokes …