Error analysis and model adaptivity for flows in gas networks

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dc.contributor.authorStolwijk, Jeroen Johannes
dc.contributor.authorMehrmann, Volker
dc.date.accessioned2020-01-15T13:20:01Z
dc.date.available2020-01-15T13:20:01Z
dc.date.issued2018-11-22
dc.description.abstractIn the simulation and optimization of natural gas flow in a pipeline network, a hierarchy of models is used that employs different formulations of the Euler equations. While the optimization is performed on piecewise linear models, the flow simulation is based on the one to three dimensional Euler equations including the temperature distributions. To decide which model class in the hierarchy is adequate to achieve a desired accuracy, this paper presents an error and perturbation analysis for a two level model hierarchy including the isothermal Euler equations in semilinear form and the stationary Euler equations in purely algebraic form. The focus of the work is on the effect of data uncertainty, discretization, and rounding errors in the numerical simulation of these models and their interaction. Two simple discretization schemes for the semilinear model are compared with respect to their conditioning and temporal stepsizes are determined for which a well-conditioned problem is obtained. The results are based on new componentwise relative condition numbers for the solution of nonlinear systems of equations. More- over, the model error between the semilinear and the algebraic model is computed, the maximum pipeline length is determined for which the algebraic model can be used safely, and a condition is derived for which the isothermal model is adequate.en
dc.description.sponsorshipDFG, TRR 154, Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerkenen
dc.identifier.eissn1844-0835
dc.identifier.issn1224-1784
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/10598
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-9524
dc.language.isoenen
dc.relation.ispartof10.14279/depositonce-7650
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subject.ddc518 Numerische Analysisde
dc.subject.othergas networken
dc.subject.otherisothermal Euler equationsen
dc.subject.otheralgebraic approximation of Euler equationsen
dc.subject.othererror analysisen
dc.subject.othercondition numberen
dc.subject.otherdata uncertaintyen
dc.subject.othercomponentwise error analysisen
dc.subject.otherstochastic error analysisen
dc.titleError analysis and model adaptivity for flows in gas networksen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.2478/auom-2018-0027en
dcterms.bibliographicCitation.issue2en
dcterms.bibliographicCitation.journaltitleAnalele științifice ale Universității Ovidius Constanța. Seria Matematicăen
dcterms.bibliographicCitation.originalpublishernameUniversitatea Ovidius din Constanţaen
dcterms.bibliographicCitation.originalpublisherplaceKonstanzaen
dcterms.bibliographicCitation.pageend266en
dcterms.bibliographicCitation.pagestart231en
dcterms.bibliographicCitation.volume26en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Mathematikde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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