A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

H Liang, Xiao-Bo Chen

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN 2] and Neumann-to-Dirichlet [ND 2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier–Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier–Laguerre expansion. © 2017 Elsevier Inc. All rights reserved.

    Original languageEnglish
    Pages (from-to)506-532
    Number of pages27
    JournalJournal of Computational Physics
    Volume347
    DOIs
    Publication statusPublished - 15 Oct 2017

    Fingerprint

    control surfaces
    Control surfaces
    floating
    Boundary integral equations
    collocation
    integral equations
    Green's function
    Green's functions
    Laguerre functions
    Orthogonal functions
    orthogonal functions
    expansion
    circumferences
    Fourier series
    dipoles
    Derivatives
    Decomposition
    decomposition
    formulations
    radii

    Cite this

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    title = "A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies",
    abstract = "A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN 2] and Neumann-to-Dirichlet [ND 2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier–Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier–Laguerre expansion. {\circledC} 2017 Elsevier Inc. All rights reserved.",
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    A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies. / Liang, H; Chen, Xiao-Bo.

    In: Journal of Computational Physics, Vol. 347, 15.10.2017, p. 506-532.

    Research output: Contribution to journalArticle

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    AU - Liang, H

    AU - Chen, Xiao-Bo

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    AB - A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN 2] and Neumann-to-Dirichlet [ND 2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier–Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier–Laguerre expansion. © 2017 Elsevier Inc. All rights reserved.

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