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Communication Dans Un Congrès Année : 2021

Dissipative Shallow Water Equations: a port-Hamiltonian formulation

Résumé

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.

Domaines

Automatique

Dates et versions

hal-04030946 , version 1 (15-03-2023)

Identifiants

Citer

Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefèvre. Dissipative Shallow Water Equations: a port-Hamiltonian formulation. 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021, Oct 2021, Berlin, Germany. pp.167-172, ⟨10.1016/j.ifacol.2021.11.073⟩. ⟨hal-04030946⟩

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