Existence and stability of regularized shock solutions, with applications to rimming flows
Autor(a) principal: | |
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Data de Publicação: | 2008 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.13/4532 |
Resumo: | This paper is concerned with regularization of shock solutions of nonlinear hyperbolic equations, i.e., introduction of a smoothing term with a coefficient ε, then taking the limit ε → 0. In addition to the classical use of regularization for eliminating physically meaningless solutions which always occur in non-regularized equa tions (e.g. waves of depression in gas dynamics), we show that it is also helpful for stability analysis. The general approach is illustrated by applying it to rimming flows, i.e., flows of a thin film of viscous liquid on the inside of a horizontal rotating cylinder, with or without surface tension (which plays the role of the regularizing effect). In the latter case, the spectrum of available linear eigenmodes appears to be continuous, but in the former, it is discrete and, most importantly, remains discrete in the limit of infinitesimally weak surface tension. The regularized (discrete) spectrum is fully determined by the point where the velocity of small perturbations vanishes, with the rest of the domain, including the shock region, being unimportant. |
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Existence and stability of regularized shock solutions, with applications to rimming flowsLiquid filmsRimming flowsShocksStabilitySurface tension.Faculdade de Ciências Exatas e da EngenhariaThis paper is concerned with regularization of shock solutions of nonlinear hyperbolic equations, i.e., introduction of a smoothing term with a coefficient ε, then taking the limit ε → 0. In addition to the classical use of regularization for eliminating physically meaningless solutions which always occur in non-regularized equa tions (e.g. waves of depression in gas dynamics), we show that it is also helpful for stability analysis. The general approach is illustrated by applying it to rimming flows, i.e., flows of a thin film of viscous liquid on the inside of a horizontal rotating cylinder, with or without surface tension (which plays the role of the regularizing effect). In the latter case, the spectrum of available linear eigenmodes appears to be continuous, but in the former, it is discrete and, most importantly, remains discrete in the limit of infinitesimally weak surface tension. The regularized (discrete) spectrum is fully determined by the point where the velocity of small perturbations vanishes, with the rest of the domain, including the shock region, being unimportant.SpringerDigitUMaBenilov, E. S.Benilov, M. S.O’Brien, S. B. G.2022-08-31T10:45:41Z2008-01-01T00:00:00Z2008-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.13/4532engBenilov, E. S., Benilov, M. S., & O’Brien, S. B. G. (2009). Existence and stability of regularized shock solutions, with applications to rimming flows. Journal of Engineering Mathematics, 63(2), 197-212. DOI: 10.1007/s10665-008-9227-110.1007/s10665-008-9227-1info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2022-09-05T12:57:52Zoai:digituma.uma.pt:10400.13/4532Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T15:08:39.677933Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Existence and stability of regularized shock solutions, with applications to rimming flows |
title |
Existence and stability of regularized shock solutions, with applications to rimming flows |
spellingShingle |
Existence and stability of regularized shock solutions, with applications to rimming flows Benilov, E. S. Liquid films Rimming flows Shocks Stability Surface tension . Faculdade de Ciências Exatas e da Engenharia |
title_short |
Existence and stability of regularized shock solutions, with applications to rimming flows |
title_full |
Existence and stability of regularized shock solutions, with applications to rimming flows |
title_fullStr |
Existence and stability of regularized shock solutions, with applications to rimming flows |
title_full_unstemmed |
Existence and stability of regularized shock solutions, with applications to rimming flows |
title_sort |
Existence and stability of regularized shock solutions, with applications to rimming flows |
author |
Benilov, E. S. |
author_facet |
Benilov, E. S. Benilov, M. S. O’Brien, S. B. G. |
author_role |
author |
author2 |
Benilov, M. S. O’Brien, S. B. G. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
DigitUMa |
dc.contributor.author.fl_str_mv |
Benilov, E. S. Benilov, M. S. O’Brien, S. B. G. |
dc.subject.por.fl_str_mv |
Liquid films Rimming flows Shocks Stability Surface tension . Faculdade de Ciências Exatas e da Engenharia |
topic |
Liquid films Rimming flows Shocks Stability Surface tension . Faculdade de Ciências Exatas e da Engenharia |
description |
This paper is concerned with regularization of shock solutions of nonlinear hyperbolic equations, i.e., introduction of a smoothing term with a coefficient ε, then taking the limit ε → 0. In addition to the classical use of regularization for eliminating physically meaningless solutions which always occur in non-regularized equa tions (e.g. waves of depression in gas dynamics), we show that it is also helpful for stability analysis. The general approach is illustrated by applying it to rimming flows, i.e., flows of a thin film of viscous liquid on the inside of a horizontal rotating cylinder, with or without surface tension (which plays the role of the regularizing effect). In the latter case, the spectrum of available linear eigenmodes appears to be continuous, but in the former, it is discrete and, most importantly, remains discrete in the limit of infinitesimally weak surface tension. The regularized (discrete) spectrum is fully determined by the point where the velocity of small perturbations vanishes, with the rest of the domain, including the shock region, being unimportant. |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008-01-01T00:00:00Z 2008-01-01T00:00:00Z 2022-08-31T10:45:41Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.13/4532 |
url |
http://hdl.handle.net/10400.13/4532 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Benilov, E. S., Benilov, M. S., & O’Brien, S. B. G. (2009). Existence and stability of regularized shock solutions, with applications to rimming flows. Journal of Engineering Mathematics, 63(2), 197-212. DOI: 10.1007/s10665-008-9227-1 10.1007/s10665-008-9227-1 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799129954755018752 |