Dissipative Shallow Water Equations: a port-Hamiltonian formulation

Authors

Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefèvre

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.

Keywords

Shallow Water Equations (SWE); Port-Hamiltonian systems (pHs); Dissipative PDEs; Partitioned Finite Element Method (PFEM)

Citation

• Journal: IFAC-PapersOnLine
• Year: 2021
• Volume: 54
• Issue: 19
• Pages: 167–172
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2021.11.073
• Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021

BibTeX

@article{Cardoso_Ribeiro_2021,
  title={{Dissipative Shallow Water Equations: a port-Hamiltonian formulation}},
  volume={54},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2021.11.073},
  number={19},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Cardoso-Ribeiro, Flávio Luiz and Matignon, Denis and Lefèvre, Laurent},
  year={2021},
  pages={167--172}
}

Download the bib file

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