Geometric and energy-aware decomposition of the Navier-Stokes equations: A port-Hamiltonian approach

Federico Califano, Ramy Rashad, Frederico P. Schuller, Stefano Stramigioli

Published 2021-03-03Version 1

A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the interconnection of the power preserving structure which underlies the motion of perfect fluids to a dissipative port which encodes Newtonian constitutive relations of shear and bulk stresses. The relevant diffusion and the boundary terms characterizing the Navier-Stokes equations on construction.