Modelling flood routing on initially dry beds with the refined treatment of wetting and drying

Abstract

Details are given of the refinement of a two-dimensional hydrodynamic model, based on a total variation diminishing finite volume method, for predicting rapid flood flows on initially dry beds. A Roe approximate Riemann solver, with the monotone upstream scheme for conservation laws (MUSCL) scheme and the procedure of predictor–corrector in time stepping, has been used in this model. The scheme is second-order accurate in both time and space and is free from spurious oscillations. The model deploys unstructured triangular grids. A wetting and drying approach, originally developed for a regular grid finite difference model, has been refined to suit the triangular grid finite volume model. The model was first verified against analytical solutions and experimental data of dam-break flows on initially dry beds, with favourable agreement being obtained between the model predictions and measurements. The model was then employed to simulate flood propagations in a large flood detention basin in China and in an urban region in the UK. Numerical model tests were undertaken to investigate the sensitivity of model predictions to the value of a minimum water depth as required for treating the wetting and drying fronts. It was found that the selection of the minimum water depth can have a significant impact on the speed of the flood wave propagation on an initially dry bed. For a given time step, an excessively large value of the minimum water depth would result in inaccurate predictions of the wetting and drying wave fronts, but a very small value would lead to numerical instability.