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

Flávio Luiz Cardoso-Ribeiro (1) , Ghislain Haine (2) , Laurent Lefèvre (3) , Denis Matignon (2)

1 ITA - Instituto Tecnológico de Aeronáutica [São José dos Campos]
2 Fédération ENAC ISAE-SUPAERO ONERA
3 LCIS - Laboratoire de Conception et d'Intégration des Systèmes

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.

Mots clés: Shallow Water Equations (SWE); Port-Hamiltonian Systems (pHs); Viscous Damping; Partitioned Finite Element Method (PFEM)

Domaines: Mathématiques [math]

Flávio Luiz Cardoso-Ribeiro, Ghislain Haine, Laurent Lefèvre, Denis Matignon. Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization. Mathematics of Control, Signals, and Systems, 2024, ⟨10.1007/s00498-024-00404-6⟩. ⟨hal-04835390⟩