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 waterdynamics. First, a port-Hamiltonian formulation is provided for the two-dimensionalrotational shallow water equations with viscous damping. Both tangential and nor-mal boundary port variables are introduced. Then,...

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Bibliographic Details
Published in:Mathematics of control, signals, and systems signals, and systems, 2024-11
Main Authors: Cardoso-Ribeiro, Flávio Luiz, Haine, Ghislain, Lefèvre, Laurent, Matignon, Denis
Format: Article
Language:English
Subjects:
Mathematics
Online Access:Get full text
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Summary:This paper is dedicated to structure-preserving spatial discretization of shallow waterdynamics. First, a port-Hamiltonian formulation is provided for the two-dimensionalrotational shallow water equations with viscous damping. Both tangential and nor-mal boundary port variables are introduced. Then, the corresponding weak form isderived and a partitioned finite element method is applied to obtain a finite-dimensionalcontinuous-time port-Hamiltonian approximation. Four simulation scenarios areinvestigated to illustrate the approach and show its effectiveness.
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-024-00404-6