Efficient Approximation of Flow Problems With Multiple Scales in Time

Lade...
Vorschaubild
Dateien
Zu diesem Dokument gibt es keine Dateien.
Datum
2020
Autor:innen
Richter, Thomas
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
DOI (zitierfähiger Link)
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Core Facility der Universität Konstanz
Gesperrt bis
Titel in einer weiteren Sprache
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published
Erschienen in
Zusammenfassung

In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier--Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on a slow scale in time. We derive an averaging scheme that is of first order with respect to the ratio of time scales $\epsilon$. In order to cope with the problem of unknown initial data for the fast-scale problem, we assume near-periodicity in time. Moreover, we construct a second-order accurate time discretization scheme and derive a complete error analysis for a corresponding simplified ODE system. The resulting multiscale scheme does not ask for the continuous simulation of the fast-scale variable and shows powerful speedups up to 1:10,000 compared to a resolved simulation. Finally, we present some numerical examples for the full Navier--Stokes system to illustrate the convergence and performance of the approach.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Konferenz
Rezension
undefined / . - undefined, undefined
Zitieren
ISO 690FREI, Stefan, Thomas RICHTER, 2020. Efficient Approximation of Flow Problems With Multiple Scales in Time. In: Multiscale Modeling & Simulation. Society for Industrial and Applied Mathematics (SIAM). 2020, 18(2), pp. 942-969. ISSN 1540-3459. eISSN 1540-3467. Available under: doi: 10.1137/19M1258396
BibTex
@article{Frei2020-05-26Effic-50387,
  year={2020},
  doi={10.1137/19M1258396},
  title={Efficient Approximation of Flow Problems With Multiple Scales in Time},
  number={2},
  volume={18},
  issn={1540-3459},
  journal={Multiscale Modeling & Simulation},
  pages={942--969},
  author={Frei, Stefan and Richter, Thomas}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/50387">
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-07-29T11:38:46Z</dcterms:available>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-07-29T11:38:46Z</dc:date>
    <dcterms:abstract xml:lang="eng">In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier--Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on a slow scale in time. We derive an averaging scheme that is of first order with respect to the ratio of time scales $\epsilon$. In order to cope with the problem of unknown initial data for the fast-scale problem, we assume near-periodicity in time. Moreover, we construct a second-order accurate time discretization scheme and derive a complete error analysis for a corresponding simplified ODE system. The resulting multiscale scheme does not ask for the continuous simulation of the fast-scale variable and shows powerful speedups up to 1:10,000 compared to a resolved simulation. Finally, we present some numerical examples for the full Navier--Stokes system to illustrate the convergence and performance of the approach.</dcterms:abstract>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Richter, Thomas</dc:creator>
    <dc:creator>Frei, Stefan</dc:creator>
    <dc:contributor>Frei, Stefan</dc:contributor>
    <dc:language>eng</dc:language>
    <dcterms:title>Efficient Approximation of Flow Problems With Multiple Scales in Time</dcterms:title>
    <dc:contributor>Richter, Thomas</dc:contributor>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/50387"/>
    <dcterms:issued>2020-05-26</dcterms:issued>
  </rdf:Description>
</rdf:RDF>
Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Kontakt
URL der Originalveröffentl.
Prüfdatum der URL
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Ja
Diese Publikation teilen