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Dissipative Shallow Water Equations: a port-Hamiltonian formulation

Cardoso-Ribeiro, Flávio Luiz and Matignon, Denis and Lefèvre, Laurent Dissipative Shallow Water Equations: a port-Hamiltonian formulation. ( In Press: 2021) In: Lagrangian and Hamiltonian Methodes for Nonlinear Control (7th LHMNC 2021), 11 October 2021 - 13 October 2021 (Berlin, Germany).

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Abstract

The dissipative Shallow Water Equations (DSWEs) are investigated as port-Hamiltonian systems. Dissipation models of different types are considered: either as nonlinear bounded operators, or as linear unbounded operators involving a classical diffusion term in 1D, or the vectorial Laplacian in 2D. In order to recast the dissipative SWE into the framework of pHs with dissipation, a physically meaningful factorization of the vectorial Laplacian is being used, which nicely separates the divergent and the rotational components of the velocity field. Finally, the structure-preserving numerical scheme provided by the Partitioned Finite Element Method (PFEM) is applied to the nonlinear bounded dissipative fluid models. For the linear unbounded cases, a change of variables is highlighted, to transform the DSWEs into a new pHs with a polynomial structure, which proves more suitable for numerics.

Item Type:Invited Conference
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université Grenoble Alpes - UGA (FRANCE)
Other partners > Instituto Tecnológico de Aeronáutica - ITA (BRASIL)
Laboratory name:
Funders:
ANR-16-CE92- 0028, INFIDHEM
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Deposited On:20 Sep 2021 14:02

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