Hamiltonian Formulation for Water Wave Equation

Sultana, Shamima; Rahman, Zillur

doi:10.4236/ojfd.2013.32010

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…Potential energy is related to the fluid pressure in the pipeline. Sultana & Rahman (2013) [18] indicated that these forms of energy involve a function that represents the energy associated with leaks. This function captures the effect of leaks on the system and can vary depending on the location and magnitude of the leaks and is used to model and quantify the hydraulic head loss owing to leaks in the pipeline.…”

Section: Hamiltonian Conservative Systemmentioning

confidence: 99%

Development of a Conservative Hamiltonian Dynamic System for the Early Detection of Leaks in Pressurized Pipelines

Ladino-Moreno,

García-Ubaque,

Zamudio-Huertas

2024

Civ Eng J

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In this study, we propose an innovative approach for real-time leakage detection in pipelines by integrating conservative Hamiltonian equations and experimental Internet of Things (IoT) technologies. The proposed method combines a hybrid model that utilizes sensors and IoT devices to acquire real-time data and solves the coupled system of Hamiltonian equations using the ODE45 numerical integration method. Spectral frequency analysis is an essential part of this method, as it reveals specific patterns in the pressure and flow signals. The findings highlighted 95% accuracy in leak detection, which was validated through a comparison of the theoretical and experimental data. The novelty of this approach lies in its ability to maintain constant total system energy, thereby enabling continuous monitoring for early leak detection. As an improvement, the proper handling of sensor signals is emphasized, underscoring its contribution to the efficient management of water resources in potable water distribution systems. Doi: 10.28991/CEJ-2024-010-04-01 Full Text: PDF

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Section: Hamiltonian Conservative Systemmentioning

confidence: 99%

Development of a Conservative Hamiltonian Dynamic System for the Early Detection of Leaks in Pressurized Pipelines

Ladino-Moreno,

García-Ubaque,

Zamudio-Huertas

2024

Civ Eng J

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“…The shallow water equations (SWE) describe the kinematic behaviour of a thin inviscid single fluid layer flowing over a variable topography. In the setting of irrotational flows and flat bottom topography, the fluid is described by a scalar potential ϕ and the canonical Hamiltonian formulation (29) is recovered [37]. The resulting Algorithm 3 Rank-adaptive reduced basis method…”

Section: Shallow Water Equationsmentioning

confidence: 99%

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

2022

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This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the full model is approximated on local reduced spaces that are adapted in time using dynamical low-rank approximation techniques. The reduced dynamics is prescribed by approximating the symplectic projection of the Hamiltonian vector field in the tangent space to the local reduced space. This ensures that the canonical symplectic structure of the Hamiltonian dynamics is preserved during the reduction. In addition, accurate approximations with low-rank reduced solutions are obtained by allowing the dimension of the reduced space to change during the time evolution. Whenever the quality of the reduced solution, assessed via an error indicator, is not satisfactory, the reduced basis is augmented in the parameter direction that is worst approximated by the current basis. Extensive numerical tests involving wave interactions, nonlinear transport problems, and the Vlasov equation demonstrate the superior stability properties and considerable runtime speedups of the proposed method as compared to global and traditional reduced basis approaches.

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“…The shallow water equations (SWE) describe the kinematic behaviour of a thin inviscid single fluid layer flowing over a variable topography. In the setting of irrotational flows and flat bottom topography, the fluid is described by a scalar potential φ and the canonical Hamiltonian formulation (8.1) is recovered [34]. The resulting time-dependent nonlinear system of PDEs is defined as…”

Section: Shallow Water Equationsmentioning

confidence: 99%

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Hesthaven¹,

Pagliantini²,

Ripamonti³

2020

Preprint

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This work proposes an adaptive structure-preserving model order reduction method for finitedimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the full model is approximated on local reduced spaces that are adapted in time using dynamical low-rank approximation techniques. The reduced dynamics is prescribed by approximating the symplectic projection of the Hamiltonian vector field in the tangent space to the local reduced space. This ensures that the canonical symplectic structure of the Hamiltonian dynamics is preserved during the reduction. In addition, accurate approximations with low-rank reduced solutions are obtained by allowing the dimension of the reduced space to change during the time evolution. Whenever the quality of the reduced solution, assessed via an error indicator, is not satisfactory, the reduced basis is augmented in the parameter direction that is worst approximated by the current basis. Extensive numerical tests involving wave interactions, nonlinear transport problems, and the Vlasov equation demonstrate the superior stability properties and considerable runtime speedups of the proposed method as compared to global and traditional reduced basis approaches.

show abstract

Hamiltonian Formulation for Water Wave Equation

Cited by 7 publications

References 20 publications

Development of a Conservative Hamiltonian Dynamic System for the Early Detection of Leaks in Pressurized Pipelines

Development of a Conservative Hamiltonian Dynamic System for the Early Detection of Leaks in Pressurized Pipelines

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

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