An Energy Stable Second-Order Accurate Scheme for Microphase Separation of Periodic Diblock Copolymers
Year: 2021
Author: Junxiang Yang, Junseok Kim
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 234–254
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.240620.071020
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 234–254
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Unconditional energy stability second-order accuracy Ohta-Kawasaki model finite difference method.