Incompressible Navier-Stokes Equation as port-Hamiltonian systems: velocity formulation versus vorticity formulation

Starting from the description of the isentropic compressible viscous fluid as port-Hamiltonian system in [Mora & al., 2020], the special cases of irrotational or incompressible cases in 2D or 3D are investigated. For the incompressible fluid, the non-linear Navier-Stokes equations are first presented with velocity as energy variable, then analyzed as a modulated port-Hamiltonian system with the help of the vorticity as energy variable. Finally, the structure- preserving numerical scheme provided by the Partitioned Finite Element Method (PFEM) of [Serhani & al., 2019] is applied to the incompressible dissipative fluid in 2D