{"title":"Numerical methods for a system of coupled Cahn-Hilliard equations","authors":"Mattia Martini, G. E. Sodini","doi":"10.2478/caim-2021-0001","DOIUrl":null,"url":null,"abstract":"Abstract In this work, we consider a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. We propose some numerical methods to approximate the solution of the system which are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our experimental approach, we present some tests and a detailed description of the numerical solutions’ behaviour obtained by varying the values of the system’s characteristic parameters.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"272 ","pages":"1 - 12"},"PeriodicalIF":0.3000,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/caim-2021-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
Abstract In this work, we consider a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. We propose some numerical methods to approximate the solution of the system which are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our experimental approach, we present some tests and a detailed description of the numerical solutions’ behaviour obtained by varying the values of the system’s characteristic parameters.
期刊介绍：
Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.
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