Abstract. We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic shell. The fluid motion is governed by the Navier-Stokes equations, while the shell is modeled by the nonlinear St. Venant-Kirchhoff constitutive law, and they are coupled together by continuity of displacement and traction (stress) along the moving mat...

Explicit boundary dissipative conditions are given for the exponential stability in L2-norm of onedimensional linear hyperbolic systems of balance laws ∂tξ + Λ∂xξ −Mξ = 0 over a finite interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint–Venant–Exner equation...

Abstract An approach is presented for directly deriving a variable parameter Muskingum method from the St. Venant equations for routing floods in channels having any shape of prismatic cross-section and flow following either Manning's or Chezy's friction law. The approach also allows the simultaneous computation of the stage hydrograph corresponding to a given inflow or the routed hydrograph. T...

We address the problem of coupling 1D St-Venant equations (Shallow Water) with 2D ones, as applied to floodplain flows (river hydraulics). Continuous coupling conditions are derived, while numerical coupling is done using optimal control processes. In a variationnal data assimilation context, this approach allows to couple both models and assimilate data simultaneously. Two different versions o...

We consider optimal control problems for the flow of gas or fresh water in pipe networks as well as drainage or sewer systems in open canals. The equations of motion are taken to be represented by the nonlinear isothermal Euler gas equations, the water hammer equations, or the St. Venant equations for flow. We formulate model hierarchies and derive an abstract model for such network flow proble...