Numerical investigations on self-similar solutions of the nonlinear diffusion equation
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Li, Yibao | - |
dc.contributor.author | Kim, Junseok | - |
dc.date.accessioned | 2021-09-05T19:27:35Z | - |
dc.date.available | 2021-09-05T19:27:35Z | - |
dc.date.created | 2021-06-15 | - |
dc.date.issued | 2013-11 | - |
dc.identifier.issn | 0997-7546 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/101662 | - |
dc.description.abstract | In this paper, we present the numerical investigations of self-similar solutions for the nonlinear diffusion equation h(t) = -(h(3)h(xxx))(x), which arises in the context of surface-tension-driven flow of a thin viscous liquid film. Here, h = h(x, t) is the liquid film height. A self-similar solution is h(x, t) = h(alpha(t)(x - x(0)) + x(0), t(0)) = f(alpha(t)(x - x(0))) and alpha(t) = [1 - 4A(t - t(0))](-1/4), where A and x(0) are constants and t(0) is a reference time. To discretize the governing equation, we use the Crank-Nicolson finite difference method, which is second-order accurate in time and space. The resulting discrete system of equations is solved by a nonlinear multigrid method. We also present efficient and accurate numerical algorithms for calculating the constants, A, x(0), and t(0). To find a self-similar solution for the equation, we numerically solve the partial differential equation with a simple step-function-like initial condition until the solution reaches the reference time to. Then, we take h(x, t(0)) as the self-similar solution f(x). Various numerical experiments are performed to show that f(x) is indeed a self-similar solution. (C) 2013 Elsevier Masson SAS. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ELSEVIER SCIENCE BV | - |
dc.subject | THIN-FILM | - |
dc.subject | LINEAR-STABILITY | - |
dc.subject | MESH REFINEMENT | - |
dc.subject | DRIVEN | - |
dc.subject | FLOW | - |
dc.subject | INSTABILITIES | - |
dc.subject | SIMULATION | - |
dc.subject | SCHEMES | - |
dc.title | Numerical investigations on self-similar solutions of the nonlinear diffusion equation | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Junseok | - |
dc.identifier.doi | 10.1016/j.euromechflu.2013.05.003 | - |
dc.identifier.scopusid | 2-s2.0-84882449695 | - |
dc.identifier.wosid | 000324283700004 | - |
dc.identifier.bibliographicCitation | EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, v.42, pp.30 - 36 | - |
dc.relation.isPartOf | EUROPEAN JOURNAL OF MECHANICS B-FLUIDS | - |
dc.citation.title | EUROPEAN JOURNAL OF MECHANICS B-FLUIDS | - |
dc.citation.volume | 42 | - |
dc.citation.startPage | 30 | - |
dc.citation.endPage | 36 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mechanics | - |
dc.relation.journalResearchArea | Physics | - |
dc.relation.journalWebOfScienceCategory | Mechanics | - |
dc.relation.journalWebOfScienceCategory | Physics, Fluids & Plasmas | - |
dc.subject.keywordPlus | THIN-FILM | - |
dc.subject.keywordPlus | LINEAR-STABILITY | - |
dc.subject.keywordPlus | MESH REFINEMENT | - |
dc.subject.keywordPlus | DRIVEN | - |
dc.subject.keywordPlus | FLOW | - |
dc.subject.keywordPlus | INSTABILITIES | - |
dc.subject.keywordPlus | SIMULATION | - |
dc.subject.keywordPlus | SCHEMES | - |
dc.subject.keywordAuthor | Thin film | - |
dc.subject.keywordAuthor | Nonlinear multigrid method | - |
dc.subject.keywordAuthor | Self-similar solution | - |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
(02841) 서울특별시 성북구 안암로 14502-3290-1114
COPYRIGHT © 2021 Korea University. All Rights Reserved.
Certain data included herein are derived from the © Web of Science of Clarivate Analytics. All rights reserved.
You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.