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Research Papers: Ocean Engineering

An Efficient Three-Dimensional FNPF Numerical Wave Tank for Large-Scale Wave Basin Experiment Simulation

[+] Author and Article Information
Solomon C. Yim

School of Civil & Construction Engineering,
Oregon State University (OSU),
Corvallis, OR 97331

Stephan T. Grilli

Department of Ocean Engineering,
University of Rhode Island (URI),
Narragansett, RI 02882

Contributed by the Ocean Offshore and Arctic Engineering Division of ASME for publication in the Journal of Offshore Mechanics and Arctic Engineering. Manuscript received May 20, 2012; final manuscript received September 6, 2012; published online February 25, 2013. Assoc. Editor: Daniel T. Valentine.

J. Offshore Mech. Arct. Eng 135(2), 021104 (Feb 25, 2013) (10 pages) Paper No: OMAE-12-1051; doi: 10.1115/1.4007597 History: Received May 20, 2012; Revised September 06, 2012

This paper presents a parallel implementation and validation of an accurate and efficient three-dimensional computational model (3D numerical wave tank), based on fully nonlinear potential flow (FNPF) theory, and its extension to incorporate the motion of a laboratory snake piston wavemaker, as well as an absorbing beach, to simulate experiments in a large-scale 3D wave basin. This work is part of a long-term effort to develop a “virtual” computational wave basin to facilitate and complement large-scale physical wave-basin experiments. The code is based on a higher-order boundary-element method combined with a fast multipole algorithm (FMA). Particular efforts were devoted to making the code efficient for large-scale simulations using high-performance computing platforms. The numerical simulation capability can be tailored to serve as an optimization tool at the planning and detailed design stages of large-scale experiments at a specific basin by duplicating its exact physical and algorithmic features. To date, waves that can be generated in the numerical wave tank (NWT) include solitary, cnoidal, and airy waves. In this paper we detail the wave-basin model, mathematical formulation, wave generation, and analyze the performance of the parallelized FNPF-BEM-FMA code as a function of numerical parameters. Experimental or analytical comparisons with NWT results are provided for several cases to assess the accuracy and applicability of the numerical model to practical engineering problems.

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Figures

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Fig. 1

Sketch of 3D-NWT geometry and parameters, for wave generation by a snake piston wavemaker (notation and details of mathematical model can be found in Sec. 3)

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Fig. 2

Snapshot of 3D-NWT simulations for the propagation of a solitary wave over constant depth in a geometry identical to that of OSU's wave basin (48.8 m long, 26.5 m wide, 0.78 m deep)

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Fig. 3

Solitary waves of target height H = (a) 0.3 m; (b) 0.45 m, in water depth h = 0.75 m. Surface elevations versus time at the wavemaker, in (—) numerical model; (-o-) OSU's 3D tank experiments (experimental data were shifted by a 0.04 s time lag; only 25% of experimental points are shown).

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Fig. 4

Solitary waves of target wave height H = (a) 0.3 m; (b) 0.45 m, in depth h = 0.75 m. Numerical (—) and experimental (-o-) surface elevations as functions of time, at three gauges at x = 8.8 m (g1), 14.9 m (g2), and 18.7 m (g3), with y = 0 (experimental data were shifted by a 0.16 s time lag; only 25% of experimental points are shown).

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Fig. 5

Solitary waves of target wave height H = (a) 0.3 m; (b) 0.45 m, in depth h = 0.75 m. Numerical (—) and experimental (-o-) water particle velocity components (u, w) as functions of time, at gauge g3 location: x = 18.7 m, y = 0, at depth z = −0.61 m (only 25% of experimental points are shown).

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Fig. 6

Cnoidal wave of target height H = 0.3 m and period T = 3.5 s, in water depth h = 0.75 m. Numerical (—) and theoretical (- - -) surface elevations at the wavemaker as functions of time.

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Fig. 7

Cnoidal wave of Fig. 6 numerical wave elevation as a function of time, at three wave gauges at x = (g1: —) 8.8 m, (g2: - - -) 14.9 m, and (g3: —.) 18.7 m, with y = 0

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Fig. 8

Cnoidal wave of Figs. 6 and 7. Numerical: (a) bottom pressure as a function of time at two gauges at x = (—) 4 and (- - -) 16 m, with y = 0; (b) wave particle velocity components u (—), w (- - -) as functions of time at gauge g3, with x = 18.7 m, y = 0, at depth z = −0.61 m.

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Fig. 9

Airy wave of target height H = 0.2 m and period T = 3.0 s, in water depth h = 0.75 m. Numerical (—) and theoretical (- - -) surface elevations at the wavemaker as functions of time.

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Fig. 10

Airy wave of Fig. 9 numerical surface elevation as a function of time, at three wave gauges at x = (g1: —) 8.8 m, (g2: - - -) 14.9 m, and (g3: —.) 18.7 m, with y = 0

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Fig. 11

Case of Figs. 9 and 10, numerical: (a) bottom pressure as a function of time at two gauges at x = (—) 4 and (- - -) 16 m, with y = 0; (b) wave particle velocity components u (—), w (- - -) as functions of time at x = 18.7 m, z = −0.61 m, y = 0

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Fig. 12

Clock time (—) and speed-up (- - -) versus number of CPUs, for five time steps of 3D-NWT simulations (Fig. 2) for application: (a) 1, using N = 2592 nodes and n = 6 FMA tree levels; (b) 2, using N = 13,838 nodes and n = 7

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Fig. 13

Clock time versus number of BEM nodes N and CPUs: 1 (- - -) or 8 (—), for five time steps of 3D-NWT simulations for various application (o) (Fig. 2), using n = (5) to (8) FMA tree levels. The straight lines (—.) and (— —) indicate clock time: ∝N1.3 and N log N, respectively.

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