An unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces

Yibao Li, Junseok Kim, Nan Wang

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper, we propose an unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. The proposed scheme, which combines a Crank–Nicolson-type scheme with a linearly stabilized splitting scheme, is second-order accurate in time. The discrete system is shown to be conservative and unconditionally energy-stable. The resulting system of discrete equations is simple to implement, and can be solved using a biconjugate gradient stabilized method. We demonstrate the performance of our proposed algorithm through several numerical experiments.

Original languageEnglish
Pages (from-to)213-227
Number of pages15
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume53
DOIs
Publication statusPublished - 2017 Dec 1

Fingerprint

Cahn-Hilliard Equation
Energy
Stabilized Methods
Crank-Nicolson
Tessellation
Gradient Method
Discrete Equations
Discrete Systems
Triangle
Linearly
Discretization
Numerical Experiment
Mesh
Experiments
Demonstrate

Keywords

  • Cahn–Hilliard equation
  • Laplace–Beltrami operator
  • Mass conservation
  • Triangular surface mesh
  • Unconditionally energy-stable

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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abstract = "In this paper, we propose an unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. The proposed scheme, which combines a Crank–Nicolson-type scheme with a linearly stabilized splitting scheme, is second-order accurate in time. The discrete system is shown to be conservative and unconditionally energy-stable. The resulting system of discrete equations is simple to implement, and can be solved using a biconjugate gradient stabilized method. We demonstrate the performance of our proposed algorithm through several numerical experiments.",
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N2 - In this paper, we propose an unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. The proposed scheme, which combines a Crank–Nicolson-type scheme with a linearly stabilized splitting scheme, is second-order accurate in time. The discrete system is shown to be conservative and unconditionally energy-stable. The resulting system of discrete equations is simple to implement, and can be solved using a biconjugate gradient stabilized method. We demonstrate the performance of our proposed algorithm through several numerical experiments.

AB - In this paper, we propose an unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. The proposed scheme, which combines a Crank–Nicolson-type scheme with a linearly stabilized splitting scheme, is second-order accurate in time. The discrete system is shown to be conservative and unconditionally energy-stable. The resulting system of discrete equations is simple to implement, and can be solved using a biconjugate gradient stabilized method. We demonstrate the performance of our proposed algorithm through several numerical experiments.

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