"NUMERICAL PROCEDURE 



To deteroine the unknown strength of the sources and sinks in Equation (14), 

 we first discretize the wetted surface of the body S with many quadrilateral 

 cleoents. Figure 3 shows the discretlzed surfaces of a spheroid. Furthermore, 

 we assume that the unknown strength of the sources and sinks, a(Q), is constant 

 on each surface element. Then Equation (14) can be written as follows 



Ti j£l °J <Q P f^ G < p i' Q P AS J - " Un li 



for i - 1, 2, .... N 



(33) 



Once the derivations of the Green function, G, are evaluated numerically, 

 Equation (33) can easily be solved for Oj. The numerical evaluation of the 

 Green function and its derivatives Is the cost difficult part, and consumes a 

 lot of computer time when running the program. 



The normal derivative of the Green function In Equation (33) can be 

 expressed as 



oG oG 6C- dG 

 — ■ » Hi + — n., + — n., 



on 5x l 5y * oz J 



(34) 



The task Is to find three derivatives of the Green function. To do this, we 

 first derive the Green function suitable to numerical evaluation. The Green 

 function, Equation (10), can be rewritten as 



i i V 2 _ a. -zu, iw + u i«_u) 



' 1 o r 2 r- e (e ^ + e 



G « j sec 6 a? * du 



r r t it J Q ll u - u 



(Lj) 



ot ~S.U, -I(iJ + U , -i'a)_U. 



+ J 1 (£ 1_JLJ? 1 du ) 



o 

 (L,) 



(35) 



10 



