

= (0,, i) + e At 



■'"T Ay 



- SrA| A,,|(z,,, - z,)0 



(27) 



The function F2i-i is the finite -difference representation of the equation of 

 continuity, given as Equation 12, and F^i is the finite -difference 

 representation of the equation for conservation of momentum, given as 

 Equation 13. Therefore, from Equations 12 and 13 the values of F2i-i and Fi^ 

 are given as Equations 26 and 27, where C-^ and C-i are constants whose values 

 depend on the values of the variables on row t J . In Equations 26 and 27, the 

 superscripts have been omitted because all subscripted variables now belong to 

 row tJ*^. The partial derivatives of Equations 26 and 27 with respect to the 

 independent variables are given below: 



^^2i-i _ 1 Ay 

 az^ 2 A t 



B,. (28) 



^^2i-i = AAZb. (29) 





e (30) 



^^2-1 - e (31) 



aCi.i 



28 



