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

Abstract

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 a general Riemannian manifold arise naturally from the proposed construction.

This is a preprint submitted to the journal of Physics of Fluids. Please do not CITE this version, but only the published manuscript

References in corpus (1)

• A Primitive Variable Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations over Surface Simplicial Meshes

Cited by in corpus (4)

• Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus
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• Energetic decomposition of Distributed Systems with Moving Material Domains: the port-Hamiltonian model of Fluid-Structure Interaction
• A differential geometric description of thermodynamics in continuum mechanics with application to Fourier-Navier-Stokes fluids