Classification of homogeneous quadratic conservation laws with viscous terms
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200005 |
Resumo: | In this paper, we study systems of two conservation laws with homogeneous quadratic flux functions. We use the viscous profile criterion for shock admissibility. This criterion leads to the occurrence of non-classical transitional shock waves, which are sensitively dependent on the form of the viscosity matrix. The goal of this paper is to lay a foundation for investigating how the structure of solutions of the Riemann problem is affected by the choice of viscosity matrix. Working in the framework of the fundamental wave manifold, we derive a necessary and sufficient condition on the model parameters for the presence of transitional shock waves. Using this condition, we are able to identify the regions in the wave manifold that correspond to transitional shock waves. Also, we determine the boundaries in the space of model parameters that separate models with differing numbers of transitional regions. |
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Classification of homogeneous quadratic conservation laws with viscous termsnonlinear non-strictly-hyperbolic conservation lawsRiemann problemsviscous profilesIn this paper, we study systems of two conservation laws with homogeneous quadratic flux functions. We use the viscous profile criterion for shock admissibility. This criterion leads to the occurrence of non-classical transitional shock waves, which are sensitively dependent on the form of the viscosity matrix. The goal of this paper is to lay a foundation for investigating how the structure of solutions of the Riemann problem is affected by the choice of viscosity matrix. Working in the framework of the fundamental wave manifold, we derive a necessary and sufficient condition on the model parameters for the presence of transitional shock waves. Using this condition, we are able to identify the regions in the wave manifold that correspond to transitional shock waves. Also, we determine the boundaries in the space of model parameters that separate models with differing numbers of transitional regions.Sociedade Brasileira de Matemática Aplicada e Computacional2007-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200005Computational & Applied Mathematics v.26 n.2 2007reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052007000200005info:eu-repo/semantics/openAccessWenstrom,Jane HurleyPlohr,Bradley J.eng2007-07-23T00:00:00Zoai:scielo:S1807-03022007000200005Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2007-07-23T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false |
dc.title.none.fl_str_mv |
Classification of homogeneous quadratic conservation laws with viscous terms |
title |
Classification of homogeneous quadratic conservation laws with viscous terms |
spellingShingle |
Classification of homogeneous quadratic conservation laws with viscous terms Wenstrom,Jane Hurley nonlinear non-strictly-hyperbolic conservation laws Riemann problems viscous profiles |
title_short |
Classification of homogeneous quadratic conservation laws with viscous terms |
title_full |
Classification of homogeneous quadratic conservation laws with viscous terms |
title_fullStr |
Classification of homogeneous quadratic conservation laws with viscous terms |
title_full_unstemmed |
Classification of homogeneous quadratic conservation laws with viscous terms |
title_sort |
Classification of homogeneous quadratic conservation laws with viscous terms |
author |
Wenstrom,Jane Hurley |
author_facet |
Wenstrom,Jane Hurley Plohr,Bradley J. |
author_role |
author |
author2 |
Plohr,Bradley J. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Wenstrom,Jane Hurley Plohr,Bradley J. |
dc.subject.por.fl_str_mv |
nonlinear non-strictly-hyperbolic conservation laws Riemann problems viscous profiles |
topic |
nonlinear non-strictly-hyperbolic conservation laws Riemann problems viscous profiles |
description |
In this paper, we study systems of two conservation laws with homogeneous quadratic flux functions. We use the viscous profile criterion for shock admissibility. This criterion leads to the occurrence of non-classical transitional shock waves, which are sensitively dependent on the form of the viscosity matrix. The goal of this paper is to lay a foundation for investigating how the structure of solutions of the Riemann problem is affected by the choice of viscosity matrix. Working in the framework of the fundamental wave manifold, we derive a necessary and sufficient condition on the model parameters for the presence of transitional shock waves. Using this condition, we are able to identify the regions in the wave manifold that correspond to transitional shock waves. Also, we determine the boundaries in the space of model parameters that separate models with differing numbers of transitional regions. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200005 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200005 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0101-82052007000200005 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
dc.source.none.fl_str_mv |
Computational & Applied Mathematics v.26 n.2 2007 reponame:Computational & Applied Mathematics instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
Computational & Applied Mathematics |
collection |
Computational & Applied Mathematics |
repository.name.fl_str_mv |
Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
repository.mail.fl_str_mv |
||sbmac@sbmac.org.br |
_version_ |
1754734889835429888 |