First- and second-order energy stable methods for the modified phase field crystal equation

Hyun Geun Lee, Jaemin Shin, June Yub Lee

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

The phase field crystal (PFC) model was extended to the modified phase field crystal (MPFC) model, which is a sixth-order nonlinear damped wave equation, to include not only diffusive dynamics but also elastic interactions. In this paper, we present temporally first- and second-order accurate methods for the MPFC equation, which are based on an appropriate splitting of the energy for the PFC equation. And we use the Fourier spectral method for the spatial discretization. The first- and second-order methods are shown analytically to be unconditionally stable with respect to the energy and pseudoenergy of the MPFC equation, respectively. Numerical experiments are presented demonstrating the accuracy and energy stability of the proposed methods.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalComputer Methods in Applied Mechanics and Engineering
Volume321
DOIs
StatePublished - 1 Jul 2017

Keywords

  • Energy stability
  • Fourier spectral method
  • Modified phase field crystal equation
  • Phase field crystal equation

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