L'utilisation des schemas de Riemann pour la solution des equations de Saint-Venant

Climatologists have warned that the significant increase in global warming will result in strong variability and extremes in precipitation patterns, a prediction that is being borne out at the present time. This implies that reservoirs equipped with spillways designed on the basis of maximum expected flood return periods ("maximum expected flood") evaluated from an analysis of historical hydrological data could prove to be dangerously inadequate to safely route extreme inflows. This combined with the advancing age of retention structures will result in an increased frequency of dam failures.; The simulation of surge wave propagation following a dam-break in a complex valley environment has become an indispensable tool in dam safety and risk assessment studies. A reliable numerical model will allow the engineer to estimate the downstream zone that will be flooded, the time of arrival of the primary surge as well as the maximum water levels and discharge that may be expected. Ultimately, early warning systems and emergency evacuation procedures maybe designed based on the model results.; The objectives of the present research is to investigate the adequacy of Riemann solvers for the simulation of such free surface flows, i.e. rapidly varying flows with moving boundaries in a geometrically complex domain. These flows occur in valleys located downstream of a dam break or in coastal areas that may be exposed to a tsunami wave.; Modeling free surface flows over domains with moving boundaries including wetting and drying areas is a challenging task. When these domains include torrential flows over complex topography the task is more difficult to handle and many existing numerical models fail to maintain numerical stability and precision.; Riemann solvers are a class of schemes suitable for modeling hyperbolic systems and have been used in gas dynamics applications for the last twenty five years. Application to the St. Venant shallow water wave equations is rather more recent and progress appears to have been made within the last fifteen years or so. These schemes are robust (an essential requirement for transcritical flows) with their expressions being physically-based and simple enough to facilitate the analyses of complex cases. They are therefore ideal candidates for high speed hydraulic free-surface flows. (Abstract shortened by UMI.)...