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Structure-Preserving Finite Volume Method for 2D Linear and Non-Linear Port-Hamiltonian Systems

Serhani, Anass and Matignon, Denis and Haine, Ghislain Structure-Preserving Finite Volume Method for 2D Linear and Non-Linear Port-Hamiltonian Systems. (2018) In: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, 1 May 2018 - 4 May 2018 (Valparaíso, Chile).

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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.

Item Type:Conference or Workshop Item (Paper)
HAL Id:hal-01793004
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited By: Ghislain Haine
Deposited On:16 May 2018 08:03

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