Analysis of Hyperbolic Systems for Mobile--Bed, Free--Surface Flow Modelling in Arbitrary Cross Sections
Tuesday 20th February 2007
Deponti, Alberto; Bonaventura, Luca; Fraccarollo, Luigi; Miglio, Edie; Rosatti, Giorgio
A model for mobile--bed river hydraulics based on the conservation equations of liquid mass, solid sediment mass and momentum is presented and analysed. The equations are reduced to one dimension by averaging over the cross section. These equations differ from the classical one--dimensional equations for mobile--bed, free--surface flows, since they take into account the effect of non--uniformities in velocity distribution along cross sections of arbitrary shape. By using appropriate closure formulae for sediment transport and for bottom friction, a system of three non--linear hyperbolic equations is obtained. Its eigenstructure is studied and its dependency on the closure formulae and on the non--dimensional parameters determining the flow and transport regimes is investigated. The existence and uniqueness of classical solutions of this hyperbolic system are discussed and an energy inequality for the frozen coefficient problem is derived.