A fully two-dimensional flux-corrected transport algorithm for hyperbolic partial differential equations
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 | Dissertation (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 | Dissertation | |
dc.type.degree | phd | |
dc.contributor.chair | Gislason, Gary | |
refterms.dateFOA | 2020-03-05T17:27:09Z |