A mathematical model for dam-break over movable bed

A four equation, one dimensional, shallow water mathematical model, suitable for the numerical simulation of dam break flow on mobile bed, is presented. Two different numerical codes, both based on the same mathematical model but on different numerical schemes, are developed: a Beam Warming, three-point backward implicit, finite difference method and a Godunov-type, high resolution, explicit finite volume method. These schemes are shown to be adequate solutions to accuracy and stability problems due to the discontinuities of the solution, the strongly time varying character of the flow, the dry/wet bed propagation phenomena and the rapid modification of the bed elevation. Numerical results for dam break flow over dry bed are compared with recent laboratory results. The maximum scour size dam is well predicted, and the hydraulic jump, induced by the strong erosion at the dam location, is reproduced. Investigation is extended to wet bed propagation, for significant values of depth ratios.