Port-Hamiltonian formulations for the modeling, simulation and control of fluids

This paper presents a state of the art on port-Hamiltonian formulations for the modeling and numerical simulation of open fluid systems. This literature review, with the help of more than one hundred classified references, highlights the main features, the positioning with respect to seminal works from the literature on this topic, and the advantages provided by such a framework. A focus is given on the shallow water equations and the incompressible Navier–Stokes equations in 2D, including numerical simulation results. It is also shown how it opens very stimulating and promising research lines towards thermodynamically consistent modeling and structure-preserving numerical methods for the simulation of complex fluid systems in interaction with their environment. • A comprehensive review of the port-Hamiltonian framework applied to fluid problems. • A modular approach to the physical modeling of fluids as open systems, including conservative or dissipative phenomena. • A structure-preserving numerical method for which the continuous power balance carries over to the discrete level. • Input/output flexibility, such as boundary stabilization by output feedback control law. • Links with irreversible processes and the first and second laws of thermodynamics.