Page 451 - Practical Design Ships and Floating Structures

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surface to facilitate the implementation of the boundary condition on the body. To concentrate grid
points next to the bow and bow surface, an exponential stretching is used in both stream-wise (4 and
transversal ('1) directions (see Figure 1)

3.3 Free Surface
The free surface is embedded in the grid generated around the ship model and its geometry is obtained
by satisfying the free surface conditions:
- pressure is equal to the atmospheric pressure everywhere on the free surface; fluid particles on the
- free surface should remain on the free surface:

3.4 Equation of Motion
The equation of motion is solved simultaneously with the Navier-Stokes equations to compute the
velocity and position of the ship. The velocity and position of the ship hull are used to impose the no-
slip condition on the body surface and to relocate the ship to generate the new grid points at each time
step. The Lax-Wendmff method and Euler explicit method were used to compute the new position
and velocity of the ship respectively. The lift coefficient CL is obtained from pressure and skin friction
distribution on the ship surface defined at previous time-step:
1
y"+' =y" +V,At +-u;At*
2

where

To start the time-marching procedure, the initial conditions are taken as:
yo =o
Vy=o

4 RESULTS
Previous work - Wanderley (2001) - described results and comparisons done for 2-D incompressible
flow around a circular cylinder. Table I reproduces some of the results presented there to demonstrate
the very good agreement that with other incompressible methods. On the other hand, the algorithm
discussed here presents a very much higher efficiency compared with other methods, lowering
significantly the computer time necessary to reach the same level of accuracy.

Applications on 3-D incompressible flow have shown the same positive performance opening concrete
possibilities for practical simulations of interest where the amount of computing time is a serious
burden. The results discussed below are still preliminary from the point of view of its scope and
validation. But they serve to evaluate the potential qualities of the proposed algorithm.
A stationary Wigley hull in incompressible flow at &=lx104 and F,= 0.25 is considered as an
illustrative example: