Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Simulation of Strongly Nonlinear Wave Generation and Wave-Body Interactions Using a 3-D Model
Simulation of Strongly Nonlinear Wave Generation and Wave-Body Interactions Using a 3-D Model
Pages 93-109
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From page 93... ...
, and the easy implementation of sophisticated numerical schemes such as higher order boundary element methods, high accuracy Taylor series expansions for the time stepping, digital filtering, spline interpolations, etc..., give the 2D MEL method the
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From page 94... ...
However, low order boundary element methods were used, with approximate treatment of free surface-body intersections and coarse discretizations, so that corresponding numerical results were merely qualitative. At the same time, more refined numerical models were developed, based on higher order panel methods, and with special attention given to the specific difficulties of the three dimensional MEL scheme, such as the accurate computation of free surface velocities and gemetry, extrapolation techniques at the intersection lines, etc...
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From page 95... ...
We describe significant results of two versions of the code differing in the formulation of the free surface motion. The first version is based on a sem~Lagrangian formulation with an explicit treatment of the incident wave through a stream function model.
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From page 96... ...
The mixed Euler-Lagrange method consists in a time stepping procedure in which the boundary value problem is solved at each time step. At a given time t, the velocity potential on the free surface (Dirichlet condition)
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From page 97... ...
This steady wave solution is used to prescribe the initial conditions, as well as the time dependent boundary conditions on the outer surface of the computational domain. At time t = 0, the potential and wave elevation given by the incident wave model are imposed on the whole boundary of the computational domain.
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From page 98... ...
Of course, the formulation described above is not universal and depends on the availability of an explicit model for the incident wave. NUMERICAL METHODS Boundary Element Method A boundary element method is used for the solution of the boundary integral equation formulation of the problem.
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From page 99... ...
In two-dimensional applications of the method, free surface grids are naturally structured, which allows a straightforward implementation of higher order finite difference or interpolation schemes for the computation of normal vectors and velocities at the free surface, in terms of the location and potential values at free surface nodes. When necessary, smoothing procedures for the removal of saw-tooth instabilities are also easily introduced.
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From page 100... ...
Full results including nonlinear time depending forces and runup on the cylinder as well as free surface maps in the vicinity of the cylinder are produced. Frequency domain coefficients for the forces and runups are then obtained by moving window Fourier analysis of the time series, and it is shown that with the adopted mesh density, stable results are obtained up to the fourth harmonics.
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From page 101... ...
With the levels of time and space discretization adopted, nonlinear simulations using ANSWAVE produce stable results up to the fourth 0.0 5.0 10.0 15.0 t ¢sqlt(c/H) Figure 1: Time series of the inline force Fx, ka = 0.20.
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From page 102... ...
ka=0.20 2A/H=0.01S l 1.5 Moving window Fourier analysis - Inline force Fx Zoom on Higher Ha'',~onics kH=X.
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From page 103... ...
ka=G.3 kH=0.8 2A/H=0.015 Figure 13: Perturbated wave elevation t=ST ka=0.3 incident waves propagates from the upper left of the plot to the opposite corner. As a conclusion to this section, we first recognize that simulations with larger amplitudes are obviously desirable, in order to illustrate the anticipated divergence between fully nonlinear modelization and perturbation analysis.
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From page 104... ...
We used 50 constant time steps per period, and the simulation was run for 10 periods. The resulting time series of the vertical displacement, velocity and acceleration are given in figure 15.
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From page 105... ...
ration was run for 1000 time steps. The fully Lagrangian formulation is used here, and we regrid the free surface at each time step with the constraint of keeping a constant difference in arc length between neighbouring nodes.
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From page 106... ...
Figure 19: t* sqrt~g/Ho)
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From page 107... ...
The first version is based on a semi Lagrangian representation of free-surface motions, with markers fixed horizontally, and is formulated in terms of a perturbation flow defined as the difference between the incident and the total flow. This splitting is possible here with fully nonlinear free surface conditions because of the characteristics of the incident wave model based on a stream function theory.
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From page 108... ...
(1995) 'Thirdorder diffraction of surface waves by a time-domain Rankine panel method', 10th Workshop on Water Waves and Floating Bodies, Oxford t29]
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From page 109... ...
Higher harmonics are negligible, but there is sensible negative vertical drift, as shown by Figure A2 representing the moving window Fourier analysis of the time series. The wave amplitude is A/H=0.025, the wave period is T*
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