Fully-Decoupled and Second-Order Time-Accurate Scheme for the Cahn–Hilliard Ohta–Kawaski Phase-Field Model of Diblock Copolymer Melt Confined in Hele–Shaw Cell  

作　　者：Junying Cao Jun Zhang Xiaofeng Yang 

机构地区：[1]School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,People’s Republic of China [2]Guizhou Key Laboratory of Big Data Statistics Analysis,Computational Mathematics Research Center,Guizhou University of Finance and Economics,Guiyang 550025,People’s Republic of China [3]Department of Mathematics,University of South Carolina,Columbia,SC,USA

出　　处：《Communications in Mathematics and Statistics》2024年第3期479-504,共26页数学与统计通讯（英文）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11901135,11961009);Foundation of Guizhou Science and Technology Department,China(Grant No.[2020]1Y015);supported by the National Natural Science Foundation of China(Nos.11901132 and 62062018);Science and Technology Program of Guizhou Province(Nos.ZK[2022]006 and ZK[2022]031);Natural Science Research Projects of Education Department of Guizhou Province(No.KY[2021]015);Guizhou Key Laboratory of Big Data Statistics Analysis(No.BDSA20200102);supported by USA National Science Foundation with Grant Number DMS-2012490.

摘　　要：In this work,we consider numerical approximations of the phase-field model of diblock copolymer melt confined in Hele–Shaw cell,which is a very complicated coupled nonlinear system consisting of the Darcy equations and the Cahn–Hilliard type equations with the Ohta–Kawaski potential.Through the combination of a novel explicit-Invariant Energy Quadratization approach and the projection method,we develop the first full decoupling,energy stable,and second-order time-accurate numerical scheme.The introduction of two auxiliary variables and the design of two auxiliary ODEs play a vital role in obtaining the full decoupling structure while maintaining energy stability.The scheme is also linear and unconditional energy stable,and the practical implementation efficiency is also very high because it only needs to solve a few elliptic equations with constant coefficients at each time step.We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process.Numerical experiments further verify the convergence rate,energy stability,and effectiveness of the developed algorithm.

关 键 词：PHASE-FIELD Explicit-IEQ DARCY Decoupled Energy Stability Diblock copolymer melt 

分 类 号：O17[理学—数学]