A Simple Benchmark Problem for the Numerical Methods of the Cahn-Hilliard Equation

Yibao Li, Chaeyoung Lee, Jian Wang, Sungha Yoon, Jintae Park, Junseok Kim

Research output: Contribution to journalArticlepeer-review

Abstract

We present a very simple benchmark problem for the numerical methods of the Cahn-Hilliard (CH) equation. For the benchmark problem, we consider a cosine function as the initial condition. The periodic sinusoidal profile satisfies both the homogeneous and periodic boundary conditions. The strength of the proposed problem is that it is simpler than the previous works. For the benchmark numerical solution of the CH equation, we use a fourth-order Runge-Kutta method (RK4) for the temporal integration and a centered finite difference scheme for the spatial differential operator. Using the proposed benchmark problem solution, we perform the convergence tests for an unconditionally gradient stable scheme via linear convex splitting proposed by Eyre and the Crank-Nicolson scheme. We obtain the expected convergence rates in time for the numerical schemes for the one-, two-, and three-dimensional CH equations.

Original languageEnglish
Article number8889603
JournalDiscrete Dynamics in Nature and Society
Volume2021
DOIs
Publication statusPublished - 2021

ASJC Scopus subject areas

  • Modelling and Simulation

Fingerprint

Dive into the research topics of 'A Simple Benchmark Problem for the Numerical Methods of the Cahn-Hilliard Equation'. Together they form a unique fingerprint.

Cite this