A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by the use of tensor-valued differential forms that allow us to 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 a general Riemannian manifold arise naturally from the proposed construction.
Geometric and energy-aware decomposition of the Navier–Stokes equations: A port-Hamiltonian approach
Federico Califano, Ramy Rashad, Frederic P. Schuller, Stefano Stramigioli; Geometric and energy-aware decomposition of the Navier–Stokes equations: A port-Hamiltonian approach. Physics of Fluids 1 April 2021; 33 (4): 047114. https://doi.org/10.1063/5.0048359
Download citation file: