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Research Papers: Offshore Technology

Fully-Nonlinear Wave-Current-Body Interaction Analysis by a Harmonic Polynomial Cell Method

[+] Author and Article Information
Yan-Lin Shao

Hydrodynamics and Stability,
DNV GL,
Høvik 1322, Norway
Department of Marine Technology,
Norwegian University of Science and Technology (NTNU),
N-7491, Trondheim, Norway
e-mail: yanlin.shao@dnv.com

Odd M. Faltinsen

Department of Marine Technology,
Norwegian University of Science and Technology (NTNU),
N-7491, Trondheim, Norway

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING Manuscript received September 26, 2013; final manuscript received February 23, 2014; published online April 1, 2014. Assoc. Editor: Thomas E. Schellin.

J. Offshore Mech. Arct. Eng 136(3), 031301 (Apr 01, 2014) (6 pages) Paper No: OMAE-13-1089; doi: 10.1115/1.4026960 History: Received September 26, 2013; Revised February 23, 2014

A new numerical 2D cell method has been proposed by the authors, based on representing the velocity potential in each cell by harmonic polynomials. The method was named the harmonic polynomial cell (HPC) method. The method was later extended to 3D to study potential-flow problems in marine hydrodynamics. With the considered number of unknowns that are typical in marine hydrodynamics, the comparisons with some existing boundary element- based methods, including the fast multipole accelerated boundary element methods, showed that the HPC method is very competitive in terms of both accuracy and efficiency. The HPC method has also been applied to study fully-nonlinear wave-body interactions; for example, sloshing in tanks, nonlinear waves over different sea-bottom topographies, and nonlinear wave diffraction by a bottom-mounted vertical circular cylinder. However, no current effects were considered. In this paper, we study the fully-nonlinear time-domain wave-body interaction considering the current effects. In order to validate and verify the method, a bottom-mounted vertical circular cylinder, which has been studied extensively in the literature, will first be examined. Comparisons are made with the published numerical results and experimental results. As a further application, the HPC method will be used to study multiple bottom-mounted cylinders. An example of the wave diffraction of two bottom-mounted cylinders is also presented.

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Figures

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Fig. 1

A set of points where the velocity potentials are known

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Fig. 2

2D multiblock grids on the free surface

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Fig. 4

Definition of the local index for a cell centered at the grid point (i, j, k) indicated as point 27 in the figure

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Fig. 3

An example of a harmonic polynomial cell containing eight hexahedron elements

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Fig. 13

Wave runup profile around the cylinders: kh = 1.0, kR = 1.0, and H = 0.06h.; Fr = 0

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Fig. 6

Linear wave amplitude around a bottom-mounted circular cylinder: kR = 1.0, kh = 1.0

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Fig. 5

Sketch of the grid system used in the analysis for the wave diffraction of a single bottom-mounted circular cylinder. The meshes are stretched in the vertical direction as the free surface moves in time. The figure is amplified seven times in the vertical direction.

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Fig. 12

Sketch of the grid system used in the analysis for the wave diffraction of two bottom-mounted circular cylinders

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Fig. 7

Wave runup profile around the cylinder: kh = 1.036, kR = 0.374, and kH = 0.122; Fr = 0.0

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Fig. 8

Wave runup profile around the cylinder: kh = 1.0, kR = 1.0, and H = 0.1h; Fr = 0.0

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Fig. 9

Wave runup profile around the cylinder: kh = 1.0, kR = 1.0, and H = 0.2h; Fr = 0.0

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Fig. 10

Wave runup profile around the cylinder: kh = 1.0, kR = 1.0, and H = 0.1h; Fr = ±0.05

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Fig. 11

Wave runup profile around the cylinder: kh = 1.0, kR = 1.0, and H = 0.2h; Fr = ±0.05

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