Numerical and physical modelling of dam-break flood waves in X-T and R-T space
The techniques for computing dam-break flood waves in prismatic channels are reviewed. Numerical models for cases with or without an initially dry downstream bed are developed. The models are based on the characteristic forms of the shallow water equations, both in (X-T) and (R-T) space, using specified time intervals and incorporating the Rankine-Hugoniot shock equations. Three numerical models for rectangular section channels are studied, namely the parallel (X-T), the expanded (R-T) and the contracted (R-T) cases; any two of these are then linked to produce three further models, described as the Contracted-Plain (RT-XT), the Contracted-Expanded (RT-RT) and the Plain-Expanded (XT-RT) models. Four physical models were tested and compared with results from the numerical models and with those from Barr and Das (1980), Marshall and Menendez (1981) and Katopodes and Schamber (1983). The numerical and experimental results are given in the form of comparative plots of front heights, surface profiles, front trajectories and depth hydrographs. Variations from the well-known solutions by Ritter (1892) and Stoker (1957), including those caused by radial flow effects are found to occur and are discussed.