A new approach for a robust solution of the fully dynamic De Saint Venant equations

A new method for the solution of the fully dynamic De Saint-Venant (DSV) equations for flood routing has been derived. The proposed methodology splits the time derivatives of the head and the flow rate in two components. The first component is found with the solution of a kinematic problem, obtained assuming the gradient of the hydrostatic force constant and equal to the value computed at the end of the previous time step. This problem is shown to have only one characteristic line and an eigenvalue equal to the average velocity. The second component is found with the solution of a perturbation problem, obtained by neglecting in the momentum equation all the terms but the flow rate time derivative and the residual gradient of the hydrostatic force. This problem is shown to have two characteristic lines and two eigenvalues equal to plus or minus the small wave celerity.