An energy stable second-order accurate scheme for microphase separation of periodic diblock copolymers

Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

Abstract

A linear, unconditionally energy stable, and second-order accurate numerical scheme for the Ohta-Kawasaki equation modeling the diblock copolymer dynamics is proposed. The temporal discretisation is based on the Crank-Nicolson temporal discretisation and extrapolation. To suppress the dominance of nonlinear term, a proper stabilising parameter is used. All nonlinear parts are linearised by using the extrapolation from the information at preceding time levels. To solve the resulting linear system, an efficient linear multigrid algorithm is used. The unconditionally energy stability, mass conservation, and unique solvability of the scheme are analytically proved. In two-dimensional case, we run convergence and stability tests, and consider pattern formations for various average concentrations. Pattern formations in three-dimensional space are also studied.

Original languageEnglish
Pages (from-to)234-254
Number of pages21
JournalEast Asian Journal on Applied Mathematics
Volume11
Issue number2
DOIs
Publication statusPublished - 2021 Feb

Keywords

  • Finite difference method
  • Ohta-Kawasaki model
  • Second-order accuracy
  • Unconditional energy stability

ASJC Scopus subject areas

  • Applied Mathematics

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