The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Two-Dimensional Numerical Modelling of Large Motions of Floating Bodies in Waves
Two-Dimensional Numerical Modelling of Large Motions of Floating Bodies in Waves
Pages 351-374
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From page 351... ...
A lowest order boundary element discretization is used. In addition to several numerical results, computations of the sway forces and the roll and heave motions induced by steep periodic waves on a floating body restrained in the sway mode are presented and compared with the results of specially conducted model tests.
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From page 352... ...
The remaining part of ED consists of two vertical geometrical control boundaries ~DC1 and ~DC2, separated by such a distance that D contains the submerged part of B A Cartesian coordinate system Oxz is chosen, with the z axis directed vertically upwards and origin O coinciding with the intersection of ~DC1 with the undisturbed free surface.
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From page 353... ...
which is a maj or concern in the considered application. The present choice of discretization scheme is founded in the belief that a 'workable ' model can be developed based on this simplest scheme, for the final task of the simulation of large motions of floating bodies in steep waves, since it is supposed that several of the anticipated problems may not necessarily be remedied by applying more refined discretizations but initially may even be obscured by the inherent difficulties of such applications.
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From page 354... ...
3.2 The Simulation of Airy Waves As a test case, the method was applied to simulate the propagation of steady Airy waves in the control domain. In the simulation, the initial values of the potential on the undisturbed free surface z ~ 0 were specified according to the Airy wave potential: /(x,t)
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From page 355... ...
The numerical solutions did not exhibit any discernible evidence of degeneration even after, for example, 400 time steps or up to 10 wave periods. 3.3 The Unsteady Wave Propagation The simulation of the propagation of unsteady waves is achieved by specifying an exciting wave potential on one of the control boundaries.
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From page 356... ...
4. The Unsteady Propagation of Steep Waves 4.1 The Evolution Equations for The Free Surface For the s imulation of the propagation of steep waves, it is necessary to consider the non-linear free surface conditions (2)
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From page 357... ...
It was found through numerical results that the form of the excitation potential has negligible influence on the generated numerical wave at points in the interior of D, provided they are sufficiently far from the upstream boundary. An alternative way of simulating waves is to provide a moving wave-maker at one end of the control domain.
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From page 358... ...
The occurrence of these oscillations can be attributed to the incompatibility of the excitation wave potential and elevation applied externally on ~DC1 with the wave potential and free surface elevation induced in D in the vicinity of IDA. In other words, the free surface conditions implicitly satisfied on the left of ~DC1 (i.
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From page 359... ...
It should be observed that in the analogous linear application, no such problem was encountered. Computations with successively higher levels of iteration in the time-integration of the free surface conditions and a close examination of the computed free surface profiles and boundary data suggest an insensitivity of the instability to the timeintegration schemes.
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From page 360... ...
The results presented above show that the simulation of unsteady steep wave propagation can be achieved by imposing an excitation potential on one of the vertical control boundaries encompass ing a rectangular fluid domain. The interior solution apppears to be not sensitive to the exact form of the potential.
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From page 361... ...
. To carry out the computations on the wetted body surface aDB, it is convenient to describe the body geometry with respect to the Gx'z' system, in which it is invariant.
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From page 362... ...
This was considered necessary due to the inadequacy of published analytical, numericalor experimental data on two-dimensional motions of floating bodies in steep waves. To the authors knowledge, no systematic two-dimensional experimental data are readily available in open literature, in which a floating body is subjected to an incident wave train such that the motions and/or waves contain significant non-linear characteristics.
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From page 363... ...
The wave field was monitored using standard twin wire wave probes of resistor type. The collected data were therefore the wave heights, the horizontal force exerted on the body and roll and heave displacements of the body.
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From page 364... ...
The heave motions correlated well, with peak-to-peak values over-predicted on the average by 5% and approximately zero phase difference. The over-predictions of roll amplitudes is believed to result from effects of fluid viscosity which were not accounted for in the numerical model.
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From page 365... ...
The extension of the basic steep wave propagation algorithm, which includes the presence of a free floating body in the control fluid domain, provided time domain simulations of body motions. In the simulations steady state motions of the body excited by steep periodic waves, preceded by short transients, were achieved.
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From page 366... ...
J ., "An Introduction Boundary Element Method. " Numerical solution of partial differential equations, J .
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From page 367... ...
Second International Workshop on Water Waves and Floating Bodies, Report.
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From page 368... ...
Fig. 4 Free surface elevations for different values of a: (L-2A, d/A-0.5, H/A'O.1, AxF/A ~ 1/24 and ~t/T:1/40)
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From page 369... ...
0.00 1.00 2.~O 3.00 4.00 5.00 6.00 7.00 8.00 9.00 t/r Fig. 6 The evolution in time of free surface elevations induced by different excitation potentials.
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From page 370... ...
~ incident WAVE _ ~ h: $' Fig. 7 Comparison of experiment and theory for w~b/2g 2 O
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From page 371... ...
~ incident .~ - 16- 16- 1~- 1~- Ik. ^- ^- ^- ~t [ " hew motlen S .- ~ 16- IL~ 1~- ~ 1~.
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From page 372... ...
As much as the kinematics of a wave maker board does not imply the linearity of the generated waves, since they satisfy the non-linear free surface conditions, the application of an Airy wave potential on the upstream boundary does not imply the linearity of the wave generated in the control fluid domain. A wave excitation 372
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From page 373... ...
Otherwise the celerity would have to be determined numerically from the solution in the control fluid domain. The source of the saw-tooth instability in the wave propagation simulation is not entirely clear.
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