Stability condition of the second-order SSP-IMEX-RK method for the Cahn-Hilliard equation

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Strong-stability-preserving (SSP) implicit-explicit (IMEX) Runge-Kutta (RK) methods for the Cahn-Hilliard (CH) equation with a polynomial double-well free energy density were presented in a previous work, specifically H. Song's "Energy SSP-IMEX Runge-Kutta Methods for the Cahn-Hilliard Equation" (2016). A linear convex splitting of the energy for the CH equation with an extra stabilizing term was used and the IMEX technique was combined with the SSP methods. And unconditional strong energy stability was proved only for the first-order methods. Here, we use a nonlinear convex splitting of the energy to remove the condition for the convexity of split energies and give a stability condition for the coefficients of the second-order method to preserve the discrete energy dissipation law. Along with a rigorous proof, numerical experiments are presented to demonstrate the accuracy and unconditional strong energy stability of the second-order method.

Original languageEnglish
Article number11
JournalMathematics
Volume8
Issue number1
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Cahn-Hilliard equation
  • Energy stability
  • Implicit-explicit methods
  • Runge-Kutta methods

Fingerprint

Dive into the research topics of 'Stability condition of the second-order SSP-IMEX-RK method for the Cahn-Hilliard equation'. Together they form a unique fingerprint.

Cite this