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    A fully two-dimensional flux-corrected transport algorithm for hyperbolic partial differential equations

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    Huang_S_1989.pdf
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    Author
    Huang, Sen-Wei
    Chair
    Gislason, Gary
    Keyword
    Mathematics
    Metadata
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    URI
    http://hdl.handle.net/11122/9325
    Abstract
    Numerical solutions of the hyperbolic partial differential equation, $\partial p\over\partial t$ + $\vec\nabla \cdot (p\vec u)$ = 0, will generally encounter the difficulties of large diffusion and oscillations near steep gradients or discontinuities. The method of Flux-Corrected Transport (FCT) developed by Boris and Book has conquered these difficulties for the one-dimensional case. Motivated by this one-dimensional FCT algorithm, a fully two-dimensional FCT algorithm is developed in this present work. This fully two-dimensional FCT algorithm is a two-step procedure: (1) the transport scheme, and (2) the antidiffusion scheme. The second step of the procedure could also be replaced by an application of the one-dimensional antidiffusion algorithm in the x direction and the y direction separately. The stability, phase shift errors and positivity for the fully two-dimensional transport scheme are analyzed. Test results are presented. The possibility of the extension of the FCT method to three dimensions are discussed.
    Description
    Dissertation (Ph.D.) University of Alaska Fairbanks, 1989
    Date
    1989
    Type
    Dissertation
    Collections
    Mathematics and Statistics

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