Mathematical modeling and parameter identification for unsteady flow in compound channels. - Abida, Habib. (University of Ottawa (Canada), 1992)
This numerical study is divided into two main parts: In the first part a model for routing unsteady flows in compound channels, called RUFICC, is developed. The model accounts for flood plain contribution to system conveyance and also for lateral momentum transfer (LMT) between adjacent deep and shallow zones of compound flow fields. In the modeling approach composite channel sections are divided into representative deep and shallow zones. The resulting one-dimensional model equations, which are a modified form of the St. Venant equations, are solved using a four-point implicit finite difference scheme. Different procedures to account for LMT in the modeling process were considered. These included empirical models that were developed based on field and laboratory measurements under steady flow conditions. The effect of LMT was found to be insignificant in most of the applications considered. For a hypothetical channel with wide and rough flood plains LMT was found to be strongest at small flood plain depths and resulted in attenuation of the discharge hydrographs. In the simulation exercises included in this work RUFICC's performance was compared to those of two frequently-used conventional models, namely: the Off-Channel Storage Model (OCSM) and the Separate Channel Model (SCM). For the applications considered a better agreement was achieved between RUFICC's simulated hydrographs and the observed data. Applying the two conventional models resulted in a marked delay in the fall of the recession curve of the simulated hydrographs. The OCSM also underestimated stages and discharges by more than 25%, especially for fairly high flood plain flows. Flood routing exercises, which involve the solution of the St. Venant equations, require that the geometric and hydraulic properties of the river reach under study be known. This includes the cross-sectional area of flow as well as the channel boundary roughness coefficients for different flow depths. The second phase of this study concerned the testing of different optimization techniques to determine the most suitable optimization algorithm(s) in the estimation of flood routing data. The algorithms considered include Powell's and Rosenbrock's methods, and the Nelder and Meade Simplex algorithm. Regular channel data as well as compound channel data were used in these exercises. The solution of the unsteady flow equations requires only cross-sectional area (A) and conveyance (K) as functions of flow depth (y). Thus, instead of following the conceptual approach of optimizing upon a channel's geometric and hydraulic parameters, optimization was performed upon abstract parameters in assumed A(y) and K(y) relationships. These types of relationships in the so-called 'Black-Box' approach would obviously speed up the computations involved in solving the unsteady flow equations. Furthermore, the relative simplicity of such relationships resulted in decreased computer times and reduced amounts of required computer storage. Estimated data using the Rosenbrock and Simplex methods were then applied to route different flood events. Simulated peak stages and discharges were in good agreement with those estimated using actual routing data. (Abstract shortened by UMI.)
Keywords: Engineering, Civil.