Moving-Boundary Port-Hamiltonian Systems
T.J. Meijer, A. Das, S. Weiland
TL;DR
This paper introduces a novel class of moving-boundary port-Hamiltonian systems for distributed parameter systems on time-varying domains, providing a theoretical foundation and a numerical discretization scheme.
Contribution
It derives the time-varying Dirac structure for such systems and establishes their port-Hamiltonian representation, enabling advanced modeling and simulation.
Findings
Derived the time-varying Dirac structure.
Established the port-Hamiltonian representation for moving boundaries.
Developed and verified a dynamic meshing discretization scheme.
Abstract
In this paper, we consider linear boundary port-Hamiltonian distributed parameter systems on a time-varying spatial domain. We derive the specific time-varying Dirac structure that these systems give rise to and use it to formally establish a new class of moving-boundary port-Hamiltonian systems by showing that these distributed parameter systems on a time-varying spatial domain admit a port-Hamiltonian representation. We demonstrate that our results can be leveraged to develop a spatial discretization scheme with dynamic meshing for approximating the telegrapher's equations on a time-varying spatial domain, which we subsequently verify numerically.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Control and Stability of Dynamical Systems