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

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.

To cite this paper:
Cardoso-Ribeiro Flávio Luiz, Haine Ghislain, Lefèvre Laurent, Matignon Denis (2025) Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization. Mathematics of Control, Signals, and Systems; 37(2):361–394

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