Hirt 



Fig. 2 - Location of flow 

 variables in a cell 



•■m 



Equations (11) are statements of the conservation of mass and momentum. 

 Our finite-difference approximations should likewise maintain these conserva- 

 tion properties. The horizontal-momentum equation is approximated with the 

 explicit-difference equation thus r.. 



1 fn+ 1 



/ 2 ^i+ 1/ 2' 



OX 



(UiV-(ui,,)^ 



, J-l/2 , J+ 1/2 



('JV)i+l/2 - ('JV)i+l/2 



+ r~(<Pi' -^i.i) + gx 



('-'i+3/2 2'-'i+ 1/ 2 ■*" "^i- 1/ 2^ 



-r("i+l/2- 2Ui+i/2 + Ui+!/2) 



(12) 



A similar approximation is used for the vertical-momentum equation, 



1 /n+ 1 j + 1/ 2 n i + 1/ 2\ 

 r: ( Vi - Vi ) 



, J + 1/2 sj + 1/2 



8y 



(viM - (vl 



i + M 



(13) 

 (Cont) 



420 



