The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Numerical Computations for a Nonlinear Free Surface Flow Problem
Numerical Computations for a Nonlinear Free Surface Flow Problem
Pages 403-420
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From page 403... ...
Main computational efforts are made for the critical Froude number, i.e., Fh = 1.0, just because of less computation time compared to the small depth Froude numbers. To treat the case of small Froude number, one simply has to take more finite elements.
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From page 405... ...
Specifically, the present variational form is obtained from Luke's form by subtracting the volume integral of the potential resulted in the process of the integration by parts with respect to time. The present variational functional has more advantage over the original Luke variational functional in treating the nonlinear free surface boundary conditions.
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From page 406... ...
3.3 Numerical Dispersion Relation. If one solves the above variational formulation numerically, one encounters the effect of numerical dispersion depending on the specific numerical schemes employed.
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This means that with lumping we can take time step three times larger than the standard finite element method without loss of the order of accuracy in the dispersion relation; The dispersion correction given in Eq.
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To reduce the contamination of the phase errors in the computational domain caused by the short wave components, an unwinding scheme by using asymmetric test function has been successfully employed as in Hughes & Brooks (1982~. The discretized form of Eq.
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From page 409... ...
In presenting our computed results,all the physical quantities are nondimensionalized by h, ph3 and for the length, mass, and time, respectively as mentioned previously. Before we made the computations for the ship in the tank, we tested the case of a two-dimensional free oscillations in a three dimensional rectangular tank as an intial-value problem.
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Fig. 6 Numerical test of the effect of unwinding parameter c2 for the convective term across the radiation boundary.
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who treated a pressure patch in Table 1. Table 2 shows the amplitude, speed and the generation period of solitons obtained in the tank reduced to one half of the tank width for several values of the blockage coefficients when Fh = 1.
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1982 A theoretical framework for Petrov-Galerkin Methods with discontinuous weighting Functions: Application to the Streamlineupwind procedure Finite Elements in Fluids, vol. 4, John Wiley & Sons Ltd., pp.
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Fig. 7 Computed free surface for Fh = 413 ~
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Fig. 8 Computed free surface for Fh = 0 9 414
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10 Computed free surface for Fh = 0 7 415
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t Fig. 12 Wave resistance for different Froude numbers (B = 4, b = 0.4)
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The comparisons are made on the linear dispersion relation and the speed of the nonlinear wave of permanent form among several different approximate theories. We present the results obtained by the equations derived by Green & Naghdi(1976)
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From page 418... ...
For L1 and L2 schemes the speed of permanent wave form can be derived using the dynamic free-surface condition and their two integral invariants, i.e., mass and momentum flux. They are given below: ON: C2 = 1 +A (A.6)
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We have admired your pioneering research on the GreenNaghdi method applied to the nonlinear freesurface flow problems. We were the comment on the dry mode, we partly agree with Professor Ertekin on the possibility of dry bottom due to the numerical instability.
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