Date of Award
4-17-1989
Document Type
Dissertation
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.
Recommended Citation
Huang, Sen-Wei, "A fully two-dimensional flux-corrected transport algorithm for hyperbolic partial differential equations" (1989). Mathematics and Statistics . 28.
https://ualaska.researchcommons.org/uaf_grad_math_stats/28
Handle
http://hdl.handle.net/11122/9325