Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.130
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dc.contributor.authorLi, Jiequan-
dc.contributor.authorMedviďová-Lukáčová, Mária-
dc.contributor.authorWarnecke, Gerald-
dc.date.accessioned2006-02-17T09:50:03Zde_DE
dc.date.available2006-02-17T09:50:03Zde_DE
dc.date.issued2003-03-
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/132-
dc.description.abstractThe subject of this paper is a demonstration of the accuracy and robustness of evolution Galerkin schemes applied to two-dimensional Riemann problems with finitely many constant states. In order to have a test case with known exact solution we consider a linear first order system for the wave equation and test evolution Galerkin methods as well as other commonly used schemes with respect to their accuracy in capturing important structural phenomena of the solution. For the two-dimensional Riemann problems with finitely many constant states some parts of the exact solution are constructed in the following three steps. Using a self-similar transformation we solve the Riemann problem outside a neighborhood of the origin and then work inwards. Next a Goursant-type problem has to be solved to describe the interaction of waves up to the sonic circle. Inside it a system of composite elliptichyperbolic type is obtained, which may not always be solvable exactly. There an interesting local maximum principle can be shown. Finally, an exact partial solution is used for numerical comparisons.en
dc.language.isoende_DE
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectgenuinely multidimensional schemesde_DE
dc.subjecthyperbolic systemsde_DE
dc.subjectwave equationde_DE
dc.subjectEuler equationsde_DE
dc.subjectevolution Galerkin schemesde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleEvolution Galerkin schemes applied to two-dimensional Riemann problems for the wave equation systemde_DE
dc.typeWorking Paperde_DE
dc.date.updated2006-03-16T11:38:01Zde_DE
dc.identifier.urnurn:nbn:de:gbv:830-opus-1912de_DE
dc.identifier.doi10.15480/882.130-
dc.type.diniworkingPaper-
dc.subject.gndHyperbolisches Systemde
dc.subject.gndGalerkin-Methodede
dc.subject.gndEvolutionsoperatorde
dc.subject.gndWellengleichungde
dc.subject.ddccode510-
dc.subject.msc65M06:Finite difference methodsen
dc.subject.msc35L05:Wave equationen
dc.subject.msccode35L05-
dc.subject.msccode65M06-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-opus-1912de_DE
tuhh.publikation.typworkingPaperde_DE
tuhh.opus.id191de_DE
tuhh.oai.showtruede_DE
dc.identifier.hdl11420/132-
tuhh.abstract.englishThe subject of this paper is a demonstration of the accuracy and robustness of evolution Galerkin schemes applied to two-dimensional Riemann problems with finitely many constant states. In order to have a test case with known exact solution we consider a linear first order system for the wave equation and test evolution Galerkin methods as well as other commonly used schemes with respect to their accuracy in capturing important structural phenomena of the solution. For the two-dimensional Riemann problems with finitely many constant states some parts of the exact solution are constructed in the following three steps. Using a self-similar transformation we solve the Riemann problem outside a neighborhood of the origin and then work inwards. Next a Goursant-type problem has to be solved to describe the interaction of waves up to the sonic circle. Inside it a system of composite elliptichyperbolic type is obtained, which may not always be solvable exactly. There an interesting local maximum principle can be shown. Finally, an exact partial solution is used for numerical comparisons.de_DE
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.130-
tuhh.type.opusResearchPaper-
tuhh.institute.germanMathematik E-10de
tuhh.institute.englishMathematics E-10en
tuhh.institute.id47de_DE
tuhh.type.id17de_DE
tuhh.gvk.hasppnfalse-
dc.type.driverworkingPaper-
dc.identifier.oclc930768234-
dc.type.casraiWorking Paper-
tuhh.relation.ispartofseriesPreprints des Institutes für Mathematikde_DE
tuhh.relation.ispartofseriesnumber58de_DE
item.grantfulltextopen-
item.creatorGNDLi, Jiequan-
item.creatorGNDMedviďová-Lukáčová, Mária-
item.creatorGNDWarnecke, Gerald-
item.openairecristypehttp://purl.org/coar/resource_type/c_8042-
item.fulltextWith Fulltext-
item.tuhhseriesidPreprints des Institutes für Mathematik-
item.openairetypeWorking Paper-
item.creatorOrcidLi, Jiequan-
item.creatorOrcidMedviďová-Lukáčová, Mária-
item.creatorOrcidWarnecke, Gerald-
item.seriesrefPreprints des Institutes für Mathematik;58-
item.languageiso639-1en-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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