UMD Theses and Dissertations

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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Duraisamy, KarthikeyanSubject: search.filters.subject.Limited Space Time Reconstruction

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    Development of a New Class of High order Implicit Non-Oscillatory Schemes for Conservation Laws
    (2004-12-03) Duraisamy, Karthikeyan; Liu, Jian-Guo; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Hyperbolic conservation laws allow for discontinuities to develop in the solution. In order to obtain non-oscillatory solutions near discontinuities and high gradient regions, numerical schemes have to satisfy conditions additional to linear stability requirements. These restrictions render high order implicit time integration schemes impractical since the allowable time-step sizes are not much higher than that for explicit schemes. In this work, an investigation is made on the factors that cause these time-step restrictions and two novel schemes are developed in an attempt to overcome the severity of these restrictions. In the first method, the order of accuracy of the {\em time integration} is lowered in high gradient and discontinuous regions. In the second method, the solution is reconstructed in {\em space and time} in a non-oscillatory manner. These concepts are evaluated on model scalar and vector hyperbolic conservation equations. The ultimate objective of this work is to develop a scheme that is accurate and unconditionally non-oscillatory.