### 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 [D_{N} ^{2}] and Neumann-to-Dirichlet [N_{D} ^{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 language | English |
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Pages (from-to) | 506-532 |

Number of pages | 27 |

Journal | Journal of Computational Physics |

Volume | 347 |

DOIs | |

Publication status | Published - 15 Oct 2017 |

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*Journal of Computational Physics*, vol. 347, pp. 506-532. https://doi.org/10.1016/j.jcp.2017.07.014

**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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

AU - Liang, H

AU - Chen, Xiao-Bo

PY - 2017/10/15

Y1 - 2017/10/15

N2 - 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.

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.

KW - Dirichlet-to-Neumann

KW - Fourier–Laguerre series

KW - Green function

KW - Irregular frequencies

KW - Multi-domain method

KW - Wave radiation/diffraction

UR - http://www.scopus.com/inward/record.url?scp=85025601282&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2017.07.014

DO - 10.1016/j.jcp.2017.07.014

M3 - Article

VL - 347

SP - 506

EP - 532

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -