Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions

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Abstract

The dynamic dam–fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under theassumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements,which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transientanalysis of fluid–structure system. Comp Struct 1979;10:383–93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element forthe dynamic analysis of fluid–solid system. Int J Numer Methods Eng 1983;19:1657–68]. The irrotational condition for inviscid fluids isimposed by the penalty method and consequentially leads to a type of micropolar media. The model is implemented using a FE code, andthe numerical results of a rectangular bidimensional basin (subjected to horizontal sinusoidal acceleration) are compared with the analyticalsolution. It is demonstrated that the Lagrangian model is able to perform pressure and gravity wave propagation analysis, even ifthe gravity (or surface) waves are dispersive. The dispersion nature of surface waves indicates that the wave propagation velocity isdependent on the wave frequency.For the practical analysis of the coupled dam–fluid problem the analysed region of the basin must be reduced and the use of suitableasymptotic boundary conditions must be investigated. The classical Sommerfeld condition is implemented by means of a boundary layerof dampers and the analysis results are shown for the cases of sinusoidal forcing.The classical Sommerfeld condition is highly efficient for pressure-based FE modelling, but may not be considered fully adequate forthe displacement-based FE approach. In the present paper a high-order boundary condition proposed by Higdom [Higdom RL. Radiationboundary condition for dispersive waves. SIAM J Numer Anal 1994;31:64–100] is considered. Its implementation requires the resolutionof a multifreedom constraint problem, defined in terms of incremental displacements, in the ambit of dynamic time integrationproblems. The first- and second-order Higdon conditions are developed and implemented. The results are compared with the Sommerfeldcondition results, and with the analytical unbounded problem results.Finally, a number of finite element results are presented and their related features are discussed and critically compared.
Original languageEnglish
Pages (from-to)932-943
JournalDefault journal
Volume85
Publication statusPublished - 2007

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Dams
Boundary conditions
Fluids
Gravity waves
Surface waves
Wave propagation
Dynamic analysis

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computational Mechanics

Cite this

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title = "Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions",
abstract = "The dynamic dam–fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under theassumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements,which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transientanalysis of fluid–structure system. Comp Struct 1979;10:383–93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element forthe dynamic analysis of fluid–solid system. Int J Numer Methods Eng 1983;19:1657–68]. The irrotational condition for inviscid fluids isimposed by the penalty method and consequentially leads to a type of micropolar media. The model is implemented using a FE code, andthe numerical results of a rectangular bidimensional basin (subjected to horizontal sinusoidal acceleration) are compared with the analyticalsolution. It is demonstrated that the Lagrangian model is able to perform pressure and gravity wave propagation analysis, even ifthe gravity (or surface) waves are dispersive. The dispersion nature of surface waves indicates that the wave propagation velocity isdependent on the wave frequency.For the practical analysis of the coupled dam–fluid problem the analysed region of the basin must be reduced and the use of suitableasymptotic boundary conditions must be investigated. The classical Sommerfeld condition is implemented by means of a boundary layerof dampers and the analysis results are shown for the cases of sinusoidal forcing.The classical Sommerfeld condition is highly efficient for pressure-based FE modelling, but may not be considered fully adequate forthe displacement-based FE approach. In the present paper a high-order boundary condition proposed by Higdom [Higdom RL. Radiationboundary condition for dispersive waves. SIAM J Numer Anal 1994;31:64–100] is considered. Its implementation requires the resolutionof a multifreedom constraint problem, defined in terms of incremental displacements, in the ambit of dynamic time integrationproblems. The first- and second-order Higdon conditions are developed and implemented. The results are compared with the Sommerfeldcondition results, and with the analytical unbounded problem results.Finally, a number of finite element results are presented and their related features are discussed and critically compared.",
keywords = "Absorbing boundary, Dam–fluid interaction, Dynamic analysis, Lagrangian finite element",
author = "Francesco Parrinello and Guido Borino",
year = "2007",
language = "English",
volume = "85",
pages = "932--943",
journal = "Default journal",

}

TY - JOUR

T1 - Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions

AU - Parrinello, Francesco

AU - Borino, Guido

PY - 2007

Y1 - 2007

N2 - The dynamic dam–fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under theassumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements,which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transientanalysis of fluid–structure system. Comp Struct 1979;10:383–93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element forthe dynamic analysis of fluid–solid system. Int J Numer Methods Eng 1983;19:1657–68]. The irrotational condition for inviscid fluids isimposed by the penalty method and consequentially leads to a type of micropolar media. The model is implemented using a FE code, andthe numerical results of a rectangular bidimensional basin (subjected to horizontal sinusoidal acceleration) are compared with the analyticalsolution. It is demonstrated that the Lagrangian model is able to perform pressure and gravity wave propagation analysis, even ifthe gravity (or surface) waves are dispersive. The dispersion nature of surface waves indicates that the wave propagation velocity isdependent on the wave frequency.For the practical analysis of the coupled dam–fluid problem the analysed region of the basin must be reduced and the use of suitableasymptotic boundary conditions must be investigated. The classical Sommerfeld condition is implemented by means of a boundary layerof dampers and the analysis results are shown for the cases of sinusoidal forcing.The classical Sommerfeld condition is highly efficient for pressure-based FE modelling, but may not be considered fully adequate forthe displacement-based FE approach. In the present paper a high-order boundary condition proposed by Higdom [Higdom RL. Radiationboundary condition for dispersive waves. SIAM J Numer Anal 1994;31:64–100] is considered. Its implementation requires the resolutionof a multifreedom constraint problem, defined in terms of incremental displacements, in the ambit of dynamic time integrationproblems. The first- and second-order Higdon conditions are developed and implemented. The results are compared with the Sommerfeldcondition results, and with the analytical unbounded problem results.Finally, a number of finite element results are presented and their related features are discussed and critically compared.

AB - The dynamic dam–fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under theassumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements,which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transientanalysis of fluid–structure system. Comp Struct 1979;10:383–93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element forthe dynamic analysis of fluid–solid system. Int J Numer Methods Eng 1983;19:1657–68]. The irrotational condition for inviscid fluids isimposed by the penalty method and consequentially leads to a type of micropolar media. The model is implemented using a FE code, andthe numerical results of a rectangular bidimensional basin (subjected to horizontal sinusoidal acceleration) are compared with the analyticalsolution. It is demonstrated that the Lagrangian model is able to perform pressure and gravity wave propagation analysis, even ifthe gravity (or surface) waves are dispersive. The dispersion nature of surface waves indicates that the wave propagation velocity isdependent on the wave frequency.For the practical analysis of the coupled dam–fluid problem the analysed region of the basin must be reduced and the use of suitableasymptotic boundary conditions must be investigated. The classical Sommerfeld condition is implemented by means of a boundary layerof dampers and the analysis results are shown for the cases of sinusoidal forcing.The classical Sommerfeld condition is highly efficient for pressure-based FE modelling, but may not be considered fully adequate forthe displacement-based FE approach. In the present paper a high-order boundary condition proposed by Higdom [Higdom RL. Radiationboundary condition for dispersive waves. SIAM J Numer Anal 1994;31:64–100] is considered. Its implementation requires the resolutionof a multifreedom constraint problem, defined in terms of incremental displacements, in the ambit of dynamic time integrationproblems. The first- and second-order Higdon conditions are developed and implemented. The results are compared with the Sommerfeldcondition results, and with the analytical unbounded problem results.Finally, a number of finite element results are presented and their related features are discussed and critically compared.

KW - Absorbing boundary

KW - Dam–fluid interaction

KW - Dynamic analysis

KW - Lagrangian finite element

UR - http://hdl.handle.net/10447/34368

M3 - Article

VL - 85

SP - 932

EP - 943

JO - Default journal

JF - Default journal

ER -