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dc.creatorFu, Shipeng, 1975-en_US
dc.date.accessioned2008-08-29T00:14:05Z
dc.date.available2008-08-29T00:14:05Z
dc.date.created2008-05en_US
dc.date.issued2008-08-29T00:14:05Z
dc.identifierb70654608en_US
dc.identifier.urihttp://hdl.handle.net/2152/3844
dc.descriptiontext
dc.description.abstractEnvironmental flows (e.g. river and atmospheric flows) governed by the shallow water equations (SWE) are usually dominated by the advective mechanism over multiple time-scales. The combination of time dependency and nonlinear advection creates difficulties in the numerical solution of the SWE. A fully-implicit scheme is desirable because a relatively large time step may be used in a simulation. However, nonlinearity in a fully implicit method results in a system of nonlinear equations to be solved at each time step. To address this difficulty, a new method for implicit solution of unsteady nonlinear advection equations is developed in this research. This Time-Centered Split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically-nonlinear coupled equations for any number of variables. To explore its characteristics, the TCS algorithm is first applied to onedimensional problems and compared to the conventional nonlinear solution methods. The temporal accuracy and practical stability of the method is confirmed using these 1D examples. It is shown that TCS can computationally linearize unsteady nonlinear advection problems without either 1) outer iteration or 2) calculation of the Jacobian. A family of the TCS method is created in one general form by introducing weighting factors to different terms. We prove both analytically and by examples that the value of the weighting factors does not affect the order of accuracy of the scheme. In addition, the TCS method can not only computationally linearize but also decouple an equation system of coupled variables using special combinations of weighting factors. Hence, the TCS method provides flexibilities and efficiency in applications.en_US
dc.format.mediumelectronicen_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en_US
dc.subject.lcshHydrodynamics -- Mathematicsen_US
dc.subject.lcshDifferential equations -- Numerical solutionsen_US
dc.subject.lcshDiscrete-time systemsen_US
dc.titleA time-centered split for implicit discretization of unsteady advection problemsen_US
dc.description.departmentCivil, Architectural, and Environmental Engineeringen_US
dc.identifier.oclc241299236en_US
dc.type.genreThesisen_US
thesis.degree.departmentCivil, Architectural, and Environmental Engineeringen_US
thesis.degree.disciplineCivil Engineeringen_US
thesis.degree.grantorThe University of Texas at Austinen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US


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