修正Cahn-Hilliard方程的二阶BDF数值格式  

SECOND-ORDER BDF NUMERICAL SCHEME FOR MODIFIED CAHN-HILLIARD EQUATION WITH LAGRANGE MULTIPLIER

作　　者：吕旭 张建文 王旦霞 Lv Xu;Zhang Jianwen;Wang Danxia(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024)

机构地区：[1]太原理工大学数学学院,太原030024

出　　处：《高等学校计算数学学报》2023年第4期325-340,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：山西省国际合作基地与平台项目(202104041101019);山西省回国留学人员科研资助项目(No.2021-029);山西省基础研究计划(202203021211129).

摘　　要：1引言.在二元合金中,为了模拟现象学中的失稳分解[1-2],Cahn和Hilliard于1958年提出Cahn-Hilliard方程,该方程描述了二元合金在某种不稳定状态时相的分离和粗化现象,后经常被用来描述在温度降低时两种均匀的混合物所发生的相分离现象.随着理论的深入研究和现代科学技术的不断发展,该方程的应用也越来越广泛,如失稳分解问题,扩散问题,多相流中的界面动力学和双相通量等问题均可通过Cahn-Hilliard方程建立模型.经典的Cahn-Hilliard方程模型如下。In this paper we construct a second-order accurate numerical scheme for solving the modified Cahn-Hilliard equation with double well potential function.Firstly,the Lagrange multiplier is introduced to obtain the linear scheme of the modified Cahn-Hilliard equation.Secondly,by employing the mixture finite element method and the second-order BDF method,we give its fully discrete linear scheme.Then,the unconditional energy stability of the proposed scheme is derived.We also carry out the error analysis for the second-order fully discrete scheme of the modified Cahn-Hilliard equation in space and time,respectively.Finally,various benchmarks in two dimensions are presented to demonstrate the accuracy and validity for the constructed scheme.

关 键 词：扩散问题 界面动力学 二元合金 数值格式 失稳分解 CAHN-HILLIARD方程 分离现象 多相流 

分 类 号：O242[理学—计算数学]