Journal ArticleDOI
On large time-stepping methods for the Cahn--Hilliard equation
Yinnian He,Yunxian Liu,Tao Tang +2 more
- Vol. 57, Iss: 5, pp 616-628
TLDR
This work analyzes a class of large time-stepping methods for the Cahn-Hilliard equation discretized by Fourier spectral method in space and semi-implicit schemes in time and investigates the stability and convergence properties based on an energy approach.Abstract:
In this work, we will analyze a class of large time-stepping methods for the Cahn-Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches.read more
Citations
More filters
Journal ArticleDOI
Isogeometric analysis of the Cahn–Hilliard phase-field model
TL;DR: In this paper, a NURBS-based variational formulation for the Cahn-Hilliard equation was tested on two-dimensional and three-dimensional problems, and steady state solutions in two-dimensions and, for the first time, in threedimensions were presented.
Journal ArticleDOI
Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
TL;DR: First and second order temporal approximation schemes based on the “Invariant Energy Quadratization” method are developed, where all nonlinear terms are treated semi-explicitly, leading to a symmetric positive definite linear system to be solved at each time step.
Journal ArticleDOI
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation
TL;DR: This paper presents and compares two unconditionally energy stable finite-difference schemes for the phase field crystal equation and considers a new, fully second-order two-step algorithm that solves the nonlinear equations using an efficient nonlinear multigrid method.
Journal ArticleDOI
An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
TL;DR: It is found that the use of the time adaptivity cannot only resolve the steady-state solutions but also the dynamical changes of the solution accurately and efficiently.
Journal ArticleDOI
Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models
TL;DR: Numerical examples that verify the second-order accuracy, unconditional energy-stability, and superiority compared with their first-order accurate variants are presented.
References
More filters
Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Book
Navier-Stokes Equations: Theory and Numerical Analysis
TL;DR: This paper presents thediscretization of the Navier-Stokes Equations: General Stability and Convergence Theorems, and describes the development of the Curl Operator and its application to the Steady-State Naviers' Equations.
Book
Navier-Stokes Equations
TL;DR: Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.
Journal ArticleDOI
Applications of semi-implicit Fourier-spectral method to phase field equations
Long Qing Chen,Jie Shen +1 more
TL;DR: In this paper, an efficient and accurate numerical method is implemented for solving the time-dependent Ginzburg-Landau equation and the Cahn-Hilliard equation, where the time variable is discretized by using semi-implicit schemes which allow much larger time step sizes than explicit schemes; the space variables are discretised by using a Fourier-spectral method whose convergence rate is exponential in contrast to second order by a usual finite-difference method.
Related Papers (5)
Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
Chuanju Xu,Tao Tang +1 more