Sensitivity of flood-routing models to variations of momentum equation coefficients and terms
Xia, Renjie
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https://hdl.handle.net/2142/22203
Description
Title
Sensitivity of flood-routing models to variations of momentum equation coefficients and terms
Author(s)
Xia, Renjie
Issue Date
1992
Doctoral Committee Chair(s)
Yen, Ben C.
Department of Study
Civil and Environmental Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Language
eng
Abstract
The Saint-Venant equations consist of a continuity equation and a well-known dynamic wave equation. The dynamic wave equation is actually a simplification from a more complicated exact momentum equation by assuming some coefficients as constants and neglecting some terms involved in the exact momentum equation. In this study, a systematic and comprehensive investigation is conducted to detect the sensitivity of flood-routing models to the variations of the coefficients and terms in the exact momentum equation.
This study is divided into two aspects. The first one considers the impacts of the coefficients ($\beta$, k and k$\sp\prime$) on the solutions of the equations. These impacts can be obtained by comparing the solutions of the Saint-Venant equations ($\beta$ = k = k$\sp\prime$ = 1) with those of the exact momentum and continuity equations ($\beta$, k and k$\sp\prime$ have various values).
The second aspect is concerned with the relative contributions of the terms in the exact momentum equation (such as local and convective accelerations, pressure, channel slope, friction slope, and internal stresses) under various flow and downstream boundary conditions. In addition, the contribution of each term due to the variations of the coefficients ($\beta$, k and k$\sp\prime$) is also detected.
In both, different downstream boundary conditions are tested in order to investigate the downstream backwater effect which has been generally ignored by other researchers in their study of the unsteady flow simulations.
The results investigated in this study show: (a) The importance of the coefficients is in a descending order as k, k$\sp\prime$ and $\beta$. (b) The impacts of the coefficients on the solutions of the equations are greatly influenced by the channel slope and downstream boundary condition. (c) The contributions of the terms are closely related to the downstream boundary condition, and slightly influenced by the variations of the coefficients. (d) The pressure term is significant for either convectively decelerating or accelerating water surface profiles. Based on the results, criteria for proper selection of the equations (the exact momentum and continuity equations or the Saint-Venant equations) as well as the lower level approximations (the noninertia or kinematic wave model) are proposed.
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