{"title":"粘性流动的解析模型计算：积分因子法","authors":"Jehyeok Choi, Kwang Soo Cho","doi":"10.1007/s13367-025-00117-5","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a systematic method to solve viscoelastic model for viscometric flows. The method is to generalize integration factor for tensor differential equation. If the analytical solution for viscometric flow exists, then it is easier to check the validity of the constitutive equation than use of numerical solution. Our ansatz gives the analytical solutions of quasi-linear viscoelastic models, such as the upper-convected, lower-convected, and corotational Maxwell models, because they become sets of linear ordinary differential equations for viscometric flows such as simple shear and elongational flows. We expect that the integration factor method can improve the numerical algorithms for nonlinear viscoelastic models and we are in preparation of a new numerical algorithm based on the integration factor method.</p><h3>Graphical abstract</h3>\n<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":683,"journal":{"name":"Korea-Australia Rheology Journal","volume":"37 2","pages":"121 - 127"},"PeriodicalIF":2.6000,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical model calculation for viscometric flows: integration factor method\",\"authors\":\"Jehyeok Choi, Kwang Soo Cho\",\"doi\":\"10.1007/s13367-025-00117-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose a systematic method to solve viscoelastic model for viscometric flows. The method is to generalize integration factor for tensor differential equation. If the analytical solution for viscometric flow exists, then it is easier to check the validity of the constitutive equation than use of numerical solution. Our ansatz gives the analytical solutions of quasi-linear viscoelastic models, such as the upper-convected, lower-convected, and corotational Maxwell models, because they become sets of linear ordinary differential equations for viscometric flows such as simple shear and elongational flows. We expect that the integration factor method can improve the numerical algorithms for nonlinear viscoelastic models and we are in preparation of a new numerical algorithm based on the integration factor method.</p><h3>Graphical abstract</h3>\\n<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>\",\"PeriodicalId\":683,\"journal\":{\"name\":\"Korea-Australia Rheology Journal\",\"volume\":\"37 2\",\"pages\":\"121 - 127\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2025-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Korea-Australia Rheology Journal\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13367-025-00117-5\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Korea-Australia Rheology Journal","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s13367-025-00117-5","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Analytical model calculation for viscometric flows: integration factor method
We propose a systematic method to solve viscoelastic model for viscometric flows. The method is to generalize integration factor for tensor differential equation. If the analytical solution for viscometric flow exists, then it is easier to check the validity of the constitutive equation than use of numerical solution. Our ansatz gives the analytical solutions of quasi-linear viscoelastic models, such as the upper-convected, lower-convected, and corotational Maxwell models, because they become sets of linear ordinary differential equations for viscometric flows such as simple shear and elongational flows. We expect that the integration factor method can improve the numerical algorithms for nonlinear viscoelastic models and we are in preparation of a new numerical algorithm based on the integration factor method.
期刊介绍：
The Korea-Australia Rheology Journal is devoted to fundamental and applied research with immediate or potential value in rheology, covering the science of the deformation and flow of materials. Emphases are placed on experimental and numerical advances in the areas of complex fluids. The journal offers insight into characterization and understanding of technologically important materials with a wide range of practical applications.
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