Structure-Preserving Finite Volume Method for 2D Linear and Non-Linear Port-Hamiltonian Systems
Authors
Anass Serhani, Denis Matignon, Ghislain Haine
Abstract
In this work we extend the results of a high order finite volume semi-discretization for port-Hamiltonian system 1D linear case (Kotyczka (2016)) to the 2D linear case, worked on the wave equation. The existing pHs discretization methods deal only with the geometric part, in this paper we perform an adapted symplectic time stepping to get the fully discrete scheme in order to preserve both the geometrical properties and the energy aspects. We also show that staggered finite volume method carry over to a non-linear problem, the 2D irrotational shallow water equations. However, due to the non linearity and the non separability of the Hamiltonian, some difficulties arise both for the high order accuracy in the spatial discretization, and also for the symplecticity of the time integration.
Keywords
Port-Hamiltonian systems (pHs); distributed-parameter system (DPS); systems of conservation laws; structure-preserving discretization; finite volume method (FVM); symplectic integration
Citation
- Journal: IFAC-PapersOnLine
- Year: 2018
- Volume: 51
- Issue: 3
- Pages: 131–136
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2018.06.037
- Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018
BibTeX
@article{Serhani_2018,
title={{Structure-Preserving Finite Volume Method for 2D Linear and Non-Linear Port-Hamiltonian Systems}},
volume={51},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2018.06.037},
number={3},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Serhani, Anass and Matignon, Denis and Haine, Ghislain},
year={2018},
pages={131--136}
}
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