Mixed-Dimensional Geometric Coupling of Port-Hamiltonian Systems

We propose a new interconnection relation for infinite-dimensional port-Hamiltonian systems that enables the coupling of ports with different spatial dimensions by integrating over the the surplus dimensions. To show the practical relevance, we apply this interconnection to a model system of an actively cooled gas turbine blade. We also show that this interconnection relation behaves well with respect to a discretization in finite element space, ensuring its usability for practical applications.