Page 473 - Practical Design Ships and Floating Structures

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where m is the total number of field points :
is the influence function matrix with rn x rn elements ;
Am,,
R is the unknown source strength vector, 4%) be solved :
,to
Em is the known vector which contains the values of 4 at the field points on the
free surface and the values of a&/& at the field points on the body

Once Eqn. 4 is solved, V# can be evaluated onS, , and the combined free surface boundary conditions
on the free surface can be integrated in time.

The fundamental variables, p,gand L are used to nondimensionalize all the other variables, p is
the density of the fluid, g is the gravitational acceleration and L is the initial draught of the body. Thus,
t = 1.0 is the nondimensional draught : = is the nondimensional position ;
L
+
-
B
; is the nondimensional vector . , B=- is the nondimensional radius :
X
=
L L
D, is the nondimensional panel size : Y;=& + is the nondimensional body velocity
The nondimensionalized system, the bar system, will be used but bars on all the variables will be
dropped from now on. The numerical results shown in this thesis are all based on nondimensionalized
variables unless otherwise mentioned. Also, pair is the air pressure and is taken as zero. Consequently,
the nondimensional governing equation and boundary conditions are
A)=O

V@+O

4 NUMERICAL COMPUTATION RESULTS
Figs. 34 show the mesh of the free surface profiles due to the motion of the wigley ship model. The
froude no.(Fn) is 0.316. The time(t) histories shown in the figs. 34 are 0,20 respectively.
Figs. 5-6 show the mesh of the free surface profiles due to the motion of the Series 60 ship model.The
froude no.(Fn) is 0.3 16. The time (t) histories shown in the figs. 5-6 are 0,35 respectively.

5 CONCLUSIONS
The conclusions of this work are summarized as followings:
1 .The desingularization method is robust in simulating the motions of floating bodies with complicated