The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Numerical Grid Generation and Upstream Waves for Ships Moving in Restricted Waters
Numerical Grid Generation and Upstream Waves for Ships Moving in Restricted Waters
Pages 421-438
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From page 421... ...
Since the most important parameter in soliton generation by moving disturbances is the blockage coefficient, a strut can be made equivalent to a finite draft ship. A boundary-fitted curvilinear coordinate system based on elliptic equations is generated to deal with the difficulties due to the body-boundary conditions in a channel containing an arbitrarily-shaped ship boundary which extends to sea floor.
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From page 422... ...
Among several are: the dependence of soliton amplitudes on the blockage coefficient (the ratio of the cross-sectional area of the model at midships to the crosssectional area of the water mass, see Eq. (33~; the phenomenon is not associated with equipment malfunctioning; at critical and supercritical speeds a steady-state flow cannot, in general, be obtained; below critical speed soliton amplitudes die out leaving a shelf in front of the ship model; and no solitons can be generated as blockage coefficient goes to zero.
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From page 423... ...
Therefore, we choose to solve the following set ofgB equations for a constant water depth and zero atmospheric pressure (Wu [34]
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From page 424... ...
Since we will use a numerical grid-generation technique to map the physicalplane onto a regular rectangular computational plane to avoid interpolations as much as possible in satisfying the body-boundary condition, we must first transform the gB equations and the boundary and initial conditions to a moving coordinate system as shown in Fig.
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From page 425... ...
However, due to the addition of extra terms in the governing equations, numerical calculations become more complicated and intensive when one transforms the 425 equations from a physical plane to a rectangular computational plane with a (20) uniform grid.
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From page 426... ...
, The purpose of transforming the equations from an earth-bound system to a moving system was to avoid the generation of a numerical grid at each time step, thereby not allowing the time derivatives to produce extra terms. If we now apply the differential relations between the derivatives of a function in 1 (x,y)
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From page 427... ...
4. Numerical solution of gB equations and wave resistance In this Section, we present the method employed to solve the nonlinear and unsteady shallow-water equations as given in the last Section, and also, give the formulation for wave resistance.
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From page 428... ...
, and lo, tR represent the left and the right open boundaries, respectively, and 428 All denotes the surface of the computational region, remains constant within 1%, showing that numerical accuracy is very high. The gB equations are solved by a computer program which uses the grid points generated by another computer program.
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From page 429... ...
5. Conclusions The waves generated by a ship in a shallow-water channel can be modeled by numerical calculations of Boussinesq equations, and two-dimensional solitons may be generated ahead of the ship.
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From page 430... ...
and Qian, Z.-M., "Solitary Waves Generated by Ships in Restricted Waters," The 4Th. Asian Congress of Fluid Mechanics, August, Hong Kong, 4 pp., 1989.
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From page 431... ...
25. Qian, Z.-M., "Numerical Grid Generation and Nonlinear Waves Generated by a Strip in a Shallow-Water Channel," M.S.
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From page 432... ...
) , D : Difference between the calculations and experimental data, Sb: Blockage coefficient, h : Depth of undisturbed water, g : Gravitational acceleration, U : Speed of the ship, As: Amplitude of the first or second soliton, Us: Speed of the first or second soliton in earth-bound coordinates, Period of generation of solitons.
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From page 433... ...
D _ Dad 4.03.0 — A: \2.0 — >I 1.0 — 0.0 — 4.0 x/h 8.0 Figure 5. Numerically generated grid for the parabolic strut, Cases 1 and 2.
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Perspective plots of computed surface elevation (a)
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From page 435... ...
Perspective plots of computed surface elevation J Case 5 e 435
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The experimental data of surface elevation and total resistance (Test No.
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From page 437... ...
However, it is not very clear that reducing the truncation errors by using a higher order scheme will totally eliminate the continuous amplitude increases observed when one uses the gB equations. One must keep in mind that the momentum and, therefore, the energy is not exactly conserved in gB equations even if the sea floor is flat.
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