• Login
    View Item 
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Numerical transport in diffusive regimes

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    azu_td_9210295_sip1_m.pdf
    Size:
    3.529Mb
    Format:
    PDF
    Description:
    azu_td_9210295_sip1_m.pdf
    Download
    Author
    Jin, Shi.
    Issue Date
    1991
    Keywords
    Dissertations, Academic
    Civil engineering
    Advisor
    Levermore, C. David
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    In highly scattering regimes, the transport equation with anisotropic boundary conditions has a limit in which the leading behavior of its solution is determined by the solution of a diffusion equation with associated boundary conditions. In order for a numerical scheme to be effective in these regimes, it must have both a correct interior diffusion limit and a correct boundary condition limit. The behavior of several numerical methods are studied in these limits and formulas for the resulting diffusion equations and its boundary conditions are derived. Theoretic and numerical results show that with correct diffusion limits, the numerical methods will give promising results with coarse grids throughout the domain, even if the boundary layers are not resolved. We also prove that with correct diffusion limits, the numerical solutions will converge to the transport solution uniformly in ε, although the collision operators have a ε⁻¹ contribution to the truncation error that generally gives rise to a nonuniform consistency with the transport equation for small ε. In last part of this dissertation we study numerical methods for the hyperbolic systems with long time parabolic behavior. In this regime the lower order terms of the hyperbolic systems break the conservation law and the systems become parabolic. Most of the numerical methods for conservation laws fail to capture this long time behavior, as shown in our analysis. We will solve the general Riemann problem of the shallow water equations and use it to modified higher order Godunov schemes in order to capture the long time behavior of the nonlinear river equations.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Applied Mathematics
    Graduate College
    Degree Grantor
    University of Arizona
    Collections
    Dissertations

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.