Exact Solutions To The Riemann Problem Of The Shallow Water Equations

In this thesis we present the exact solutions to the Riemann problem of the homogenous shallow water equations at first.And we provide more detailed analysis of the Riemann solution of the shallow water equations with a bottom topography given by F,Alcrudo and F.Benkhaldoun[8].They classified the waves into twenty cases according to the wave property and the relative position.Finally,it leads to a set of equations to be solved by the Powell hybrid method.In fact,we can reduce it to the Riemann problem for the homogenous shallow water equations for some cases.However,since the approach leads to too many cases, it turns out to be so expensive that it is difficult to be used in Godunov-type schemes.