Author(s): D. Violeau; C. Peyrard; E. Dombre
Linked Author(s): Damien Violeau
Keywords: Numerical models; Time integrator; Symplectic integrator; Hamiltonian flow; Oscillation
Abstract: The time integration of hydroinformatic systems can be done through many ways, including explicit, semi-explicit or implicit methods of various orders. A specific class of numerical integrators has been recently brought to the attention of the scientific community: symplectic integrators. They are relevant in case of Hamiltonian systems, i. e. mechanical systems which can be written in terms of the Hamilton dynamic equations. Symplectic schemes ensure that the total energy is preserved in spite of the approximations due to the time discretization. In case of dissipative systems, the consequence is that the amount of lost energy is correct, in other words that the time marching scheme is not responsible for artificial energy dissipation. This has important consequences on the long-term consistency of the numerical predictions for many practical hydraulic systems. Examples are provided here, namely: 1) mass oscillations in a surge tank, 2) oscillations of a rigid body anchored with a spring and 3) free oscillations of a floating device.