Port-Hamiltonian discretization for open channel flows

Pasumarthy, Ramkrishna; Ambati, V.R.; Schaft, A.J. van der

doi:10.1016/j.sysconle.2012.05.003

Cited by 11 publications

(7 citation statements)

References 18 publications

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“…For the rotational case, a slightly modified version of (1) can be defined, that takes into account the vorticity of the fluid, see e.g., [20,23]:…”

Section: ) Shallow Water Equations With Viscous Dampingmentioning

confidence: 99%

Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization

Cardoso-Ribeiro,

Haine,

Lefèvre

et al. 2024

Preprint

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This paper is dedicated to structure-preserving spatial discretization of shallow water dynamics. First, a port-Hamiltonian formulation is provided for the two-dimensional rotational shallow water equations with viscous damping. Both tangential and normal boundary port variables are introduced. Then the corresponding weak form is derived and a partitioned finite element method is applied to obtain a finite-dimensional continuous-time port-Hamiltonian approximation. Four simulation scenarios are investigated to illustrate the approach and show its effectiveness.

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“…For the rotational case, a slightly modified version of (1) can be defined, that takes into account the vorticity of the fluid, see e.g., [20,23]:…”

Section: ) Shallow Water Equations With Viscous Dampingmentioning

confidence: 99%

Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization

Cardoso-Ribeiro,

Haine,

Lefèvre

et al. 2024

Preprint

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“…The work of Golo et al (2004) was extended to the case of a non-constant SDS in Pasumarthy et al (2012); Pasumarthy & van der Schaft (2006a) for the shallow water equations and extended to irreversible pH systems in Baaiu et al (2009b); Voß & Weiland (2011). Another method that was inspired by Golo et al (2004) is Bassi et al (2007), which was formulated for the functional analytic formulation of pH systems discussed in section 2.2.…”

Section: Discretizationmentioning

confidence: 99%

Twenty years of distributed port-Hamiltonian systems: a literature review

Rashad

Califano

Schaft

2020

IMA Journal of Mathematical Control and Information

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The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups.

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“…Apart from the model order-and complexity reduction-method proposed in [14], also, e.g., the discretization schemes in [33], [26], [42], [9], [40] can be considered to be of this category.…”

Section: Approximation Of the Hamiltonianmentioning

confidence: 99%

On port-Hamiltonian approximation of a nonlinear flow problem on networks

Liljegren-Sailer¹,

Marheineke²

2020

Preprint

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This paper is on the systematic development of robust and online-efficient approximations for a class of nonlinear partial differential equations on networks. The class includes, e.g., gas pipe network systems described by one-dimensional barotropic Euler equations. All steps necessary in nonlinear model reduction are covered by our analysis. These are the space discretization by conventional methods, the projection-based model order reduction and the complexity reduction of nonlinearities. Special attention is paid to the structure-preservation on all levels. The proposed reduced models are shown to be locally mass conservative, to fulfill energy bounds and to inherit port-Hamiltonian structure. The main ingredients of our analysis are energy-based modeling concepts like the port-Hamiltonian framework and the theory on the Legendre transform, which allow a convenient and general line of argumentation. Moreover, the case of the barotropic Euler equations is examined in more detail and a well-posedness result is proven for their approximation in our framework.

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Port-Hamiltonian discretization for open channel flows

Cited by 11 publications

References 18 publications

Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization

Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization

Twenty years of distributed port-Hamiltonian systems: a literature review

On port-Hamiltonian approximation of a nonlinear flow problem on networks

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