The Use Of Symplectic Time Integrators In Hydroinformatics.

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Damien Violeau, Christophe Peyrard, Emmanuel Dombre

Thursday 2 july 2015

11:00 - 11:15h at Oceania (level 0)

Themes: (T) Water engineering, (ST) Computational methods

Parallel session: 11E. Engineering - Computational

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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 consistency of the numerical predictions for many practical hydraulic systems. Examples will be provided, namely: 1) lagrangian methods for CFD, 2) mass oscillations in a surge tank and 3) floating device on a wave train. It will be shown how a symplectic integrators can improve significantly the model prediction, and that they are sometimes necessary to avoid spurious behaviour of the numerical computations