The most effective simulations of
complete physical problems consist of the evaluation of maximum water levels
and discharges that may be attained at particular locations during the
development of an exceptional meteorological event. There is also the previsionof the scenario subsequent to the almost instantaneous release of a greatvolume of liquid. The situation is that of the breaking of a man made dam.
There is therefore a necessity to develop a model capable of reproducing
solutions of the complete equations despite the irregularities of a
non-prismatic bed. This requires the development of efficient and effective
numerical schemes able to predict water levels and discharges in hydraulic
systems. The use of mathematical models as a predictive tool in the simulationof free surface flows represents a good candidate for the application of manyof the techniques developed in fluid dynamics. In this paper we develop a 1-D
complete model of shallow water equations with source terms using both
conservation of water mass and conservation of the momentum content of the
water. We describe the Lax-Wendroff scheme for these nonlinear partial
differential equations (PDEs) and we analyze the stability restriction of the
method.