Energy-based Modeling and Simulation of Shallow Water Waves in a Tube with Moving Boundary

Abstract

Modeling and simulation of shallow water waves in a tube with moving boundary and arbitrary cross-section are considered. Based on the a variational formulation of the well known one dimensional Saint-Venant equations in material fixed coordinates, energy-conserving finite-dimensional approximations are directly derived by the principle of least action. A particular discretization scheme is investigated, namely, a piecewise constant approximation of the distributed variables. The approach is validated in simulation and compared with alternative discretization-schemes.