Port-Hamiltonian modeling of ideal fluid flow: Part II. Compressible and incompressible flow

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

doi:10.1016/j.geomphys.2021.104199

Cited by 19 publications

(36 citation statements)

References 7 publications

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“…there is zero power flowing through the port (p, 0). Notice that this Lagrangian multiplier completely characterises the static pressure in the tensor T , which is indeed not dependent on any thermodynamic potential in the incompressible case [5].…”

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

confidence: 94%

“…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%

“…Furthermore, the boundary port (e ∂1 , f ∂1 ) characterises the power due to variation of the boundary ∂B t as described in (16)(17)(18). As a matter of fact notice that (27) is the specialisation for incompressible fluids of the general power balance for systems with moving domains described in (5), where the moving domain is expressed by the variation of ∂B t (moving with velocity u) only since we assumed ∂V to be fixed.…”

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%

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

confidence: 94%

“…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%

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

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Califano,

Rashad,

Schuller

et al. 2021

Preprint

Self Cite

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“…Since they are closed under interconnection (this feature stems from the properties of the Dirac structure [11]), pH systems have the potential to tackle complex multiphysical engineering applications. So far they were employed to model fluid-structure coupled phenomena [12], reactive flows [13], Euler and Navier-Stokes equations [14,15,16], thin mechanical and thermomecanical structures [17,18]. The interested reader may consult [19] for a comprehensive review on distributed pH systems.…”

Section: Introductionmentioning

confidence: 99%

Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus

Brugnoli¹,

Rashad²

2022

Preprint

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In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation laws and cope with mixed open boundary conditions using a single computational mesh. The possibility of including open boundary conditions allows for modular composition of complex multi-physical systems whereas the exterior calculus formulation provides a coordinate-free treatment. Our approach relies on a dual-field representation of the physical system that is redundant at the continuous level but eliminates the need of mimicking the Hodge star operator at the discrete level. By considering the Stokes-Dirac structure representing the system together with its adjoint, which embeds the metric information directly in the codifferential, the need for an explicit discrete Hodge star is avoided altogether. By imposing the boundary conditions in a strong manner, the power balance characterizing the Stokes-Dirac structure is then retrieved at the discrete level via symplectic Runge-Kutta integrators based on Gauss-Legendre collocation points. Numerical experiments validate the convergence of the method and the conservation properties in terms of energy balance both for the wave and Maxwell equations in a three dimensional domain. For the latter example, the magnetic and electric fields preserve their divergence free nature at the discrete level.

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Intrinsic Nonlinear Elasticity: An Exterior Calculus Formulation

et al. 2023

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In this paper, we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate of strain, as intensive vector-valued forms, while kinetics variables, such as stress and momentum, as extensive covector-valued pseudo-forms. We treat the spatial, material and convective representations of the motion and show how to geometrically convert from one representation to the other. Furthermore, we show the equivalence of our exterior calculus formulation to standard formulations in the literature based on tensor calculus. In addition, we highlight two types of structures underlying the theory: first, the principal bundle structure relating the space of embeddings to the space of Riemannian metrics on the body and how the latter represents an intrinsic space of deformations and second, the de Rham complex structure relating the spaces of bundle-valued forms to each other.

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Port-Hamiltonian modeling of ideal fluid flow: Part II. Compressible and incompressible flow

Cited by 19 publications

References 7 publications

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

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

Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus

Intrinsic Nonlinear Elasticity: An Exterior Calculus Formulation

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