The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Calculation of Nonlinear Water Waves around a 2-Dimensional Body in Uniform Flow by Means of Boundary Element Method
Calculation of Nonlinear Water Waves around a 2-Dimensional Body in Uniform Flow by Means of Boundary Element Method
Pages 225-238
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From page 225... ...
If we neglect viscosity and assume irrotational motion, a numerical scheme based on the less complex boundary integral equation cart be employed, which does not need high performance computers. For the problem of two dimensional free surface flow, Longuet-Higgins and Cokelet t1]
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From page 226... ...
On each boundary element divided by these nodal points, it is assumed that the complex velocity potential w varies linearly in z. Using the well known procedures by means of these linear boundary elements, the following discrete expressions are obtained with respect to eq.
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1 can Gove according to the uniform flow component, the treatment of the downstream boundary is more difficult. If this boundary is fixed, nodal points on the downstream free surface will move out of the calculation region.
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From page 228... ...
8 n ~ UP-STREAM D I FFERENCE / DO`N-STRERM D I FFEREN~ u.u- I.0 2.0 3.0 4.0 Fig. 5 Wave drag coefficients based on the schemes of upstream difference and downstream difference.
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From page 229... ...
For the first example, ejects of the time interval are exemplified. The wave drag coefficients for the cases of lit = 0.03, 0.05, 0.07 do not show serious differences caused by the time interval ~ Fig.
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From page 230... ...
~ U = 0.5m/sec ~ 4. Rectangular Floating Body with Semi-infinite Length 4.1 Treatment for Numerical Computations As described in section 3.1, tile means of solving some numerical difficulties have to be given also for this problem.
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The predicted wave profiles at final time step by three schemes of downstream difference, upstream difference and centered difference are shown in Fig.
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0.9 0-~:: 0.3; it/ UP-STREAM D I FFERENCE / ~ CENTERED D I FFERENCE Fig. 20 Wave drag coefficients based on the schemes of upstream and centered difference.
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obtained the wave profile ill front of the rectangular body by a perturbation method based on small Froude number expansion.
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From page 234... ...
and by Grosenbaugl~ and Yeung. 5.Conclusiot1 In the present study, flee simulation method of two dimensional nonlinear water waves based on BEM and the mixed Eulerian-Lagrangian approach is applied to two wave making problems around a body ifs uniform flow; the sen~i-circular mound in shallow water and the rectangular floating body with semi-infinite length.
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on Naval Hydrodynamics (1970~.
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From page 236... ...
In the present method, the combined technique of the upstream difference approximation of dw/dz, the replacement of nodal points on the free surface and the employment of the linear solution form at the downstream boundary can be expected as the numerical radiation condition.
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From page 237... ...
You have tried various difference schemes in your paper and the final choice was made from computational results. We do not understand how one can choose a specific finite difference scheme if we don't know the correct result in advance.
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