Port-Hamiltonian modeling of ideal fluid flow: Part I. Foundations and kinetic energy

Rashad, Ramy; Califano, Federico; Schüller, F.

doi:10.1016/j.geomphys.2021.104201

Cited by 19 publications

(15 citation statements)

References 11 publications

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“…The reduction procedure takes the Lagrangian description on the semidirect product Lie group to an Eulerian/spatial description on the dual of its semidirect product Lie algebra. A Lie algebra isomorphism between the reduced phase space and a space of differential forms enables the straightforward generalization of the Lie-Poisson structure to a Stokes-Dirac structure and thus also the generalization of the Hamiltonian model of ideal compressible fluid motion to a port-Hamiltonian model, see Rashad et al (2021a). This permits the consideration of spatial domains with permeable boundaries and it enables the extension of the model through interconnection with other port-Hamiltonian systems.…”

Section: Kinetic Energy Subsystemmentioning

confidence: 99%

Exergetic Port-Hamiltonian Systems: Navier-Stokes-Fourier Fluid

Lohmayer¹,

Leyendecker²

2022

Preprint

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The Exergetic Port-Hamiltonian Systems modeling language combines a graphical syntax inspired by bond graphs with a port-Hamiltonian semantics akin to the GENERIC formalism. The syntax enables the modular and hierarchical specification of the composition pattern of lumped and distributed-parameter models. The semantics reflects the first and second law of thermodynamics as structural properties. Interconnected and hierarchically defined models of multiphysical thermodynamic systems can thus be expressed in a formal language accessible to humans and computers alike. We discuss a composed model of the Navier-Stokes-Fourier fluid on a fixed spatial domain as an example of an open distributed-parameter system. At the top level, the system comprises five subsystems which model kinetic energy storage, internal energy storage, thermal conduction, bulk viscosity, and shear viscosity.

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Section: Kinetic Energy Subsystemmentioning

confidence: 99%

Exergetic Port-Hamiltonian Systems: Navier-Stokes-Fourier Fluid

Lohmayer¹,

Leyendecker²

2022

Preprint

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“…represent the flow and effort variables of the energy storage subsystem, respectively. The effort variables of the storage (also called co-energy variables) are given by [4,5]:…”

Section: Port-hamiltonian Model Of Incompressible Viscous Flow On a M...mentioning

confidence: 99%

“…Another advantage is that the complete port-Hamiltonian decomposition allows to analyse the power flow between all system components in order to de-rive conclusions on the stability of a sophisticated multi-component system [2] or to devise novel numerical algorithms that exploit the associated conservation laws subsystem by subsystem [3]. In other words, the present work allows to extend the port-Hamiltonian description of our previous fluid models [4,5,6] to the fluid-structure interaction model in Section 4.…”

Section: Introductionmentioning

confidence: 99%

Energetic decomposition of Distributed Systems with Moving Material Domains: the port-Hamiltonian model of Fluid-Structure Interaction

Califano,

Rashad,

Schuller

et al. 2021

Preprint

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We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains. The first part of the paper aims at introducing the differential geometric tools needed to represent infinite-dimensional systems on time-varying spatial domains in a port-based framework. A throughout description on the way we extend the structure presented in the seminal work [1], where only fixed spatial domains were considered, is carried through. As application of the proposed structure, we show how to model in a completely coordinate-free way the 3D fluid-structure interaction model for a rigid body immersed in an incompressible viscous flow as an interconnection of open dynamical subsystems.

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“…As part of the background material used in this work, we will compactly present and point out the main properties of covariant field equations of continuum mechanics, whose treatment is distilled from the foundational references 1,[3][4][5][6][7][8] , which inspired more recent works (e.g., [9][10][11][12] ) aiming at investigating specific geometric structure underlying the equations. a) Electronic mail: f.califano@utwente.nl…”

Section: Introductionmentioning

confidence: 99%

A differential geometric description of thermodynamics in continuum mechanics with application to Fourier–Navier–Stokes fluids

Califano

Rashad

2022

Physics of Fluids

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A description of thermodynamics for continuum mechanical systems is presented in the coordinate-free language of differential geometry. First, a careful description of the mathematical tools that are needed to formulate the relevant conservation laws is given. Second, following an axiomatic approach, the two thermodynamic principles will be described, leading to a consistent description of entropy creation mechanisms on manifolds. Third, a specialisation to Fourier-Navier-Stokes fluids will be carried through.

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Port-Hamiltonian modeling of ideal fluid flow: Part I. Foundations and kinetic energy

Cited by 19 publications

References 11 publications

Exergetic Port-Hamiltonian Systems: Navier-Stokes-Fourier Fluid

Exergetic Port-Hamiltonian Systems: Navier-Stokes-Fourier Fluid

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

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