The mitigation of the impacts to the greatest possible degree requires modelling of the ﬂood with sufﬁcient detail so as to capture both the spatial and temporal evolutions of the ﬂood event (Jorgenson, 2004), as well of the velocity ﬁeld. The selection of an appropriate model to correctly simulate dam-break ﬂood routing is therefore an essential step.
Traditionally, one and two-dimensional models have been used to model dam break ﬂooding, but these models are limited in their ability to capture the ﬂood spatial extent, in terms of ﬂow depth and velocity and timing of ﬂood arrival and recession, with any degree of detail. The development in the last years has led to several numerical models aimed at solving the so-called dam break problem (Soarez Frazao, 2002). The Concerted Action on Dam Break Modelling (CADAM) project (Morris,1998), has been set in motion by the European Union to investigate current methods and use in simulating and predicting the effects of dam failures. The obtained results show that shallow water scheme is reasonably suitable for the representation of free surface sharp transient (Wang et al., 2000) and the authors concluded that shallow water methods agree satisfactorily with experimental results (Alcrudo, 1998).
Earlier studies were primarily based on analytical solutions for idealist conditions. For example, Stoker developed an analytical solution to predict dam break flows in an idealisted channel, in which the bed slope was assumed to be zero and...
... middle of paper ...
...yperbolic problems. Afshar and Shobeyri studied the effect of irregularity of domain discretization on the performance of the CDLS method for the solution of convection-dominated problems. They concluded that their proposed CDLS method was able to produce highly accurate results for hyperbolic problems even on highly irregular distribution of nodes. This method was later used for simulation of free surface problems by Shobeyri and Afshar. They employed a priori error estimator to improve the efficiency of simulating free surface flows problems with CDLS method.
In this paper schemes was examined for the solution of the one dimensional homogeneous shallow water wave equations using the meshless associated with approximate collocated discrete least square (CDLSM) method. Then a well-known analytical solution to the dam-break problem was used to assess the performance.
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