Port-Hamiltonian modelling of fluid dynamics models with variable cross-section

Many single- and multi-phase fluid dynamical systems are governed by non-linear evolutionary equations. A key aspect of these is that the typically flows across spatially temporally varying cross-sections. We, first, show not any choice state-variables may be apt for obtaining a port-Hamiltonian realization under cross-section. We propose modified then represent in representations. define representations spatial variation cross-section with respect to new proposed state-dependent extended Stokes- Dirac structure. Finally, we account temporal variations obtain suitable structure respects properties, such as, instance, property dissipation inequality.