This video is my presentation on the paper “Exterior and Vector Calculus Views of Incompressible Navier-Stokes Port-Hamiltonian Models” at the 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control 2021 (LHMNC21), in Berlin, Germany.
The 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNC21) at the Technical University of Berlin wants to bring together control experts from different areas to exchange on physical structures as the foundation of versatile design methods, to discuss new approaches for modeling, analysis and control design, and to present state-of-the-art results on applications to complex dynamical engineering systems. With the first paper on port-Hamiltonian systems appeared in 1992, the workshop is also an ideal occasion to celebrate in special sessions the (almost) 30th anniversary of this successful framework.
Rashad, R., Califano, F., Brugnoli, A., Schuller, F. P., & Stramigioli, S. (2021). Exterior and vector calculus views of incompressible Navier-Stokes port-Hamiltonian models. IFAC-papersonline, 54(19), 173-179.
In this paper we address the modeling of incompressible Navier-Stokes equations in the port-Hamiltonian framework. Such model not only allows describing the energy dissipation due to viscous effects but also incorporates the non-zero energy exchange through the boundary of the spatial domain for generic boundary conditions. We present in this work the coordinate-free representations of this port-Hamiltonian model using both exterior calculus and vector calculus as well as their corresponding coordinate-based descriptions.