Author(s): Dongfang Liang; Roger A. Falconer; Chunbo Jiang; Xiaolin Wang
Keywords: Flood routing; Supercritical flow; Dam-break; Shock-capturing; Numerical model; River Thames
Abstract: The accurate prediction of floodwater flow is becoming more and more important as an increasing trend is evident in the frequency and intensity of flood disasters. A highly efficient shock-capturing numerical model has been developed to solve the Shallow Water Equations (SWEs) for modelling flood flows. The predictor-corrector MacCormack scheme forms the basis of the present numerical method, accompanied by a five-point, symmetrical, Total Variation Diminishing (TVD) modification in the corrector step. The resulting method has the ability to capture flood fronts, where the water level and velocity vary rapidly. Authors’ numerical tests have shown that the current computational model needs only slightly over 50% longer run time than the traditional model using the Alternating Direction Implicit (ADI) scheme, so the present shock-capturing model can be used in practical flood management. Two levee-breach experiments, i. e. the flood after a levee breach and the flood wave interaction with a circular cylinder, are employed to test the capability of the model in predicting fast flows. The computational results agree well with the experimental data. The model is finally applied to a hypothetical levee-breach flood in the Greenwich peninsular by the River Thames, which includes uneven topographies and moving boundaries. This example demonstrates the applicability of the present TVD-MacCormack model for simulating practical flood flows.