dc.contributor.author Huang, Sen-Wei dc.date.accessioned 2018-08-08T01:46:44Z dc.date.available 2018-08-08T01:46:44Z dc.date.issued 1989 dc.identifier.uri http://hdl.handle.net/11122/9325 dc.description Thesis (Ph.D.) University of Alaska Fairbanks, 1989 dc.description.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. dc.subject Mathematics dc.title A fully two-dimensional flux-corrected transport algorithm for hyperbolic partial differential equations dc.type Thesis dc.type.degree phd dc.contributor.chair Gislason, Gary refterms.dateFOA 2020-03-05T17:27:09Z
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