Simple modelling of dam failure in a natural river

Abstract

The complex problem of dam failure and subsequent flood estimation is considered. Numerical models are required and distinctive features of natural rivers such as friction and real topography have to be considered. When treating regions of rapidly varied flow, shock-capturing methods are useful and the Saint-Venant equations, in conservative form, should be employed. A number of explicit second-order two-step schemes exist, such as the ‘upwind schemes’. They require non-linear limiters, such as ‘total variation diminishing’ limiters (TVD), to prevent numerical oscillations. ‘High resolution schemes’ are obtained and complex routines have to be implemented. Run time can be burdensome even for one-dimensional calculations. Thus, in this article a very easy to implement scheme, the diffusive scheme, is considered . Stability and accuracy of the numerical solution are analysed and the performances in terms of water depths are tested. The Malpasset dam-break case (France, 1959) is referred to as a test case. Numerical results are compared with the depth measurements of a physical model and with the results of two other numerical models available in the literature.