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

TL;DR

This paper introduces a coordinate-independent port-Hamiltonian framework for compressible Newtonian fluids, capturing the geometric and energetic structure of Navier-Stokes equations on Riemannian manifolds.

Contribution

It develops a novel geometric port-Hamiltonian model for fluid dynamics that naturally incorporates dissipation and boundary effects on curved spaces.

Findings

Provides a tensor-valued differential forms formulation

Derives Navier-Stokes boundary and diffusion terms naturally

Enables geometric and energy-aware analysis of fluid flows

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.