,., , Desai and Lieber 



upon which of the two sets of equations leads to the least number of iterations 

 necessary to secure sufficient convergence, we can now decide as to the appro- 

 priateness of one over the other. 



Let us first write down explicitly the governing equations for iterations up 

 to n = 3. We shall call equations for n = o the Base Equations. The sets of 

 equations as written down below correspond to the symbolic Eqs. (1.36) and 

 (1.37). 



BASE EQUATIONS (n = 0) 



dt ^ "° Br ^ r 3^ r 2 Br ^ Re \ 3r2 ^ ^ Br r2 ^ r^ B02 ^2 ^0 / 



!^ + u !l^ + 1° ?^ + ^ - - 1.^ + ± ("-li + i ?^ - — + A !!^ + 2 !^' 



Bt ^ "° Br ^ •" 30 + r - 2r B5 ^ Re \ Br 2 ^ r Br r2 ^ r^ B02 ^ j.^ B0 < 



+— + 7 = 0; (1.21a) 



Br '^ "^ 30 



V2>/; = ; (1.22a) 



where 





These are the equations for a potential flow. The first two equations are 

 Euler's equations. 



FIRST ITERATION EQUATIONS (n=l) 



Bu . 

 Bt 



542 



