Time-Scale Decoupling for Nearly Periodic Advection-Diffusion Equations

Aart van Harten

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    Abstract

    An advection-diffusion problem is considered with an O(ɛ) perturbed T-periodic flow and O(ɛ) diffusivity, where ɛ > 0 denotes a small parameter. Such problems arise in tidally induced transport of constituents. An asymptotic approximation of the solution with O(ɛ) accuracy on a long O(l/ɛ)-time scale is constructed by using a rigorous averaging method. The averaged problem on the long time scale is completely decoupled from the O(1) time scale of the nearly periodic flow. As a consequence, numerical computations of the solution of the approximate problem can be based on a much larger time step than for the original problem. Thus a large factor is gained in numerical efficiency. In addition, piling up of discretization errors in the averaged problem is less severe than for numerical computations for the original problem. When this rigorous averaging procedure is used, two aspects of domain decomposition of the space-time cylinder play a role.
    Original languageEnglish
    Title of host publicationAsymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters
    EditorsHans G. Kaper, Marc Garbey, Gail W. Pieper
    Place of PublicationDordrecht
    PublisherSpringer
    Pages21-39
    ISBN (Print)0-7923-2061-1
    DOIs
    Publication statusPublished - 11 Feb 1993
    EventWorkshop on Asymptotic-Induced Numerical Methods for Partial Differential Equations, Critical Parameters, and Domain Decomposition - Beaune, France
    Duration: 25 May 199228 May 1992

    Publication series

    NameNATO Science Series C
    PublisherSpringer
    Volume384
    ISSN (Print)0377-2071

    Conference

    ConferenceWorkshop on Asymptotic-Induced Numerical Methods for Partial Differential Equations, Critical Parameters, and Domain Decomposition
    CountryFrance
    CityBeaune
    Period25/05/9228/05/92

    Keywords

    • METIS-125609

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