Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization

Authors

Flávio Luiz Cardoso-Ribeiro, Ghislain Haine, Laurent Lefèvre, Denis Matignon

Abstract

This paper is dedicated to structure-preserving spatial discretization of shallow water dynamics. First, a port-Hamiltonian formulation is provided for the two-dimensional rotational shallow water equations with viscous damping. Both tangential and normal boundary port variables are introduced. Then, the corresponding weak form is derived and a partitioned finite element method is applied to obtain a finite-dimensional continuous-time port-Hamiltonian approximation. Four simulation scenarios are investigated to illustrate the approach and show its effectiveness.

Keywords

Shallow water equations (SWE); Port-Hamiltonian systems (pHs); Viscous damping; Partitioned finite element method (PFEM); 76D55; 35Q35; 76M10

Citation

• Journal: Mathematics of Control, Signals, and Systems
• Year: 2024
• Volume:
• Issue:
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00498-024-00404-6

BibTeX

@article{Cardoso_Ribeiro_2024,
  title={{Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization}},
  ISSN={1435-568X},
  DOI={10.1007/s00498-024-00404-6},
  journal={Mathematics of Control, Signals, and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Cardoso-Ribeiro, Flávio Luiz and Haine, Ghislain and Lefèvre, Laurent and Matignon, Denis},
  year={2024}
}

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