The phase field method for geometric moving interfaces and their numerical approximations
This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
Basic principles and practical applications of the Cahn–Hilliard equation
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 …
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 …
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
Springtails (Collembola) are wingless arthropods adapted to cutaneous respiration in
temporarily rain-flooded habitats. They immediately form a plastron, protecting them against …
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
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 …
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
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 …
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 …
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 …
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 …
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 …
fluids in a two-dimensional bounded domain. The model consists of a Navier–Stokes …