The variational 2D Boussinesq model for wave propagation over a shoal

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    Abstract

    The Variational Boussinesq Model (VBM) for waves (Klopman et al. 2010) is based on the Hamiltonian structure of gravity surface waves. In its approximation, the fluid potential in the kinetic energy is approximated by the sum of its value at the free surface and a linear combination of vertical profiles with horizontal spatially dependent functions as coefficients. The vertical profiles are chosen a priori and determine completely the dispersive property of the model. For coastal applications, the 1D version of the model has been implemented in Finite Element with piecewise linear basis functions and has been compared with experiments from MARIN hydrodynamic laboratory for focusing wave group running above a flat bottom (Lakturov et al. 2011) and for irregular waves running above a sloping bottom (Adytia and Groesen 2011). The 2D version of the model has been derived and implemented using a pseudo-spectral method with a rectangular grid in Klopman et al. 2007, 2010. A limitation of the later implementation is a lack of flexibility when the model deals with a complicated domain such as a harbour. Here, we will present an implementation of the model in 2D Finite Element which consistent with the derivation of the model via the variational formulation. To illustrate the accuracy of wave refraction and diffraction over a complex bathymetry, the experiment of Berkhoff et al. 1982 is used to compare the FE results with measurements.
    Original languageEnglish
    Title of host publicationDevelopments in Marine CFD 2011
    Subtitle of host publicationProceedings
    Place of PublicationLondon
    PublisherThe Royal Institution of Naval Architects
    Pages25-29
    Number of pages5
    ISBN (Print)978-1-905040-92-6
    Publication statusPublished - 18 Nov 2011
    EventInternational Conference on Developments in Marine CFD 2011 - Chennai, India
    Duration: 18 Nov 201119 Nov 2011

    Conference

    ConferenceInternational Conference on Developments in Marine CFD 2011
    CountryIndia
    CityChennai
    Period18/11/1119/11/11

    Fingerprint

    wave propagation
    vertical profile
    wave group
    refraction
    bathymetry
    gravity wave
    surface wave
    diffraction
    kinetic energy
    harbor
    experiment
    hydrodynamics
    fluid

    Keywords

    • METIS-285039
    • IR-79680
    • EWI-21346
    • Variational Boussinesq
    • Shoal
    • Finite element

    Cite this

    Adytia, D., & van Groesen, E. W. C. (2011). The variational 2D Boussinesq model for wave propagation over a shoal. In Developments in Marine CFD 2011: Proceedings (pp. 25-29). London: The Royal Institution of Naval Architects.
    Adytia, D. ; van Groesen, Embrecht W.C. / The variational 2D Boussinesq model for wave propagation over a shoal. Developments in Marine CFD 2011: Proceedings. London : The Royal Institution of Naval Architects, 2011. pp. 25-29
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    title = "The variational 2D Boussinesq model for wave propagation over a shoal",
    abstract = "The Variational Boussinesq Model (VBM) for waves (Klopman et al. 2010) is based on the Hamiltonian structure of gravity surface waves. In its approximation, the fluid potential in the kinetic energy is approximated by the sum of its value at the free surface and a linear combination of vertical profiles with horizontal spatially dependent functions as coefficients. The vertical profiles are chosen a priori and determine completely the dispersive property of the model. For coastal applications, the 1D version of the model has been implemented in Finite Element with piecewise linear basis functions and has been compared with experiments from MARIN hydrodynamic laboratory for focusing wave group running above a flat bottom (Lakturov et al. 2011) and for irregular waves running above a sloping bottom (Adytia and Groesen 2011). The 2D version of the model has been derived and implemented using a pseudo-spectral method with a rectangular grid in Klopman et al. 2007, 2010. A limitation of the later implementation is a lack of flexibility when the model deals with a complicated domain such as a harbour. Here, we will present an implementation of the model in 2D Finite Element which consistent with the derivation of the model via the variational formulation. To illustrate the accuracy of wave refraction and diffraction over a complex bathymetry, the experiment of Berkhoff et al. 1982 is used to compare the FE results with measurements.",
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    Adytia, D & van Groesen, EWC 2011, The variational 2D Boussinesq model for wave propagation over a shoal. in Developments in Marine CFD 2011: Proceedings. The Royal Institution of Naval Architects, London, pp. 25-29, International Conference on Developments in Marine CFD 2011, Chennai, India, 18/11/11.

    The variational 2D Boussinesq model for wave propagation over a shoal. / Adytia, D.; van Groesen, Embrecht W.C.

    Developments in Marine CFD 2011: Proceedings. London : The Royal Institution of Naval Architects, 2011. p. 25-29.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

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    N2 - The Variational Boussinesq Model (VBM) for waves (Klopman et al. 2010) is based on the Hamiltonian structure of gravity surface waves. In its approximation, the fluid potential in the kinetic energy is approximated by the sum of its value at the free surface and a linear combination of vertical profiles with horizontal spatially dependent functions as coefficients. The vertical profiles are chosen a priori and determine completely the dispersive property of the model. For coastal applications, the 1D version of the model has been implemented in Finite Element with piecewise linear basis functions and has been compared with experiments from MARIN hydrodynamic laboratory for focusing wave group running above a flat bottom (Lakturov et al. 2011) and for irregular waves running above a sloping bottom (Adytia and Groesen 2011). The 2D version of the model has been derived and implemented using a pseudo-spectral method with a rectangular grid in Klopman et al. 2007, 2010. A limitation of the later implementation is a lack of flexibility when the model deals with a complicated domain such as a harbour. Here, we will present an implementation of the model in 2D Finite Element which consistent with the derivation of the model via the variational formulation. To illustrate the accuracy of wave refraction and diffraction over a complex bathymetry, the experiment of Berkhoff et al. 1982 is used to compare the FE results with measurements.

    AB - The Variational Boussinesq Model (VBM) for waves (Klopman et al. 2010) is based on the Hamiltonian structure of gravity surface waves. In its approximation, the fluid potential in the kinetic energy is approximated by the sum of its value at the free surface and a linear combination of vertical profiles with horizontal spatially dependent functions as coefficients. The vertical profiles are chosen a priori and determine completely the dispersive property of the model. For coastal applications, the 1D version of the model has been implemented in Finite Element with piecewise linear basis functions and has been compared with experiments from MARIN hydrodynamic laboratory for focusing wave group running above a flat bottom (Lakturov et al. 2011) and for irregular waves running above a sloping bottom (Adytia and Groesen 2011). The 2D version of the model has been derived and implemented using a pseudo-spectral method with a rectangular grid in Klopman et al. 2007, 2010. A limitation of the later implementation is a lack of flexibility when the model deals with a complicated domain such as a harbour. Here, we will present an implementation of the model in 2D Finite Element which consistent with the derivation of the model via the variational formulation. To illustrate the accuracy of wave refraction and diffraction over a complex bathymetry, the experiment of Berkhoff et al. 1982 is used to compare the FE results with measurements.

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    Adytia D, van Groesen EWC. The variational 2D Boussinesq model for wave propagation over a shoal. In Developments in Marine CFD 2011: Proceedings. London: The Royal Institution of Naval Architects. 2011. p. 25-29