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) …
The scalar auxiliary variable (SAV) approach for gradient flows
We propose a new approach, which we term as scalar auxiliary variable (SAV) approach, to
construct efficient and accurate time discretization schemes for a large class of gradient …
construct efficient and accurate time discretization schemes for a large class of gradient …
Energy-decaying extrapolated RK--SAV methods for the Allen--Cahn and Cahn--Hilliard equations
We construct and analyze a class of extrapolated and linearized Runge--Kutta (RK)
methods, which can be of arbitrarily high order, for the time discretization of the Allen--Cahn …
methods, which can be of arbitrarily high order, for the time discretization of the Allen--Cahn …
Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
How to develop efficient numerical schemes while preserving energy stability at the discrete
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …
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 …
A phase-field moving contact line model with soluble surfactants
A phase-field moving contact line model is presented for a two-phase system with soluble
surfactants. With the introduction of some scalar auxiliary variables, the original free energy …
surfactants. With the introduction of some scalar auxiliary variables, the original free energy …
Efficient numerical scheme for a dendritic solidification phase field model with melt convection
C Chen, X Yang - Journal of Computational Physics, 2019 - Elsevier
In this paper, we consider numerical approximations for a dendritic solidification phase field
model with melt convection in the liquid phase, which is a highly nonlinear system that …
model with melt convection in the liquid phase, which is a highly nonlinear system that …
On a novel fully decoupled, second-order accurate energy stable numerical scheme for a binary fluid-surfactant phase-field model
X Yang - SIAM Journal on Scientific Computing, 2021 - SIAM
The binary fluid surfactant phase-field model, coupled with two Cahn--Hilliard equations and
Navier--Stokes equations, is a very complex nonlinear system, which poses many …
Navier--Stokes equations, is a very complex nonlinear system, which poses many …
A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystals
The hydrodynamic Q-tensor model has been used for studying flows of liquid crystals and
liquid crystal polymers. It can be derived from a variational approach together with the …
liquid crystal polymers. It can be derived from a variational approach together with the …
Unconditionally energy-stable finite element scheme for the chemotaxis-fluid system
In this paper, we first deduce an improved chemotaxis-fluid system by introducing a
chemotactic stress force, which can be used to describe the chemotactic movement of …
chemotactic stress force, which can be used to describe the chemotactic movement of …