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arXiv · 2103.02277

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

Federico Califano·Ramy Rashad·Frederic P. Schuller·Stefano Stramigioli
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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.

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Federico Califano, Ramy Rashad, Frederic P. Schuller, Stefano Stramigioli. 2021-03-03. Geometric and energy-aware decomposition of the Navier-Stokes equations: A port-Hamiltonian approach. https://doi.org/10.1063/5.0048359

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