



















j+1 



















At 





M 











' 



0At 





j 



i 





Ay _ 















( 1 1 1— 







- y 



i-1 i i+1 



Distance along Channel 



Figure 4. Computation grid on the y - t plane 



and 



^^^ = [aii + l,j + 1) - a{i,j + l)]e-^ + [a(i + l,j) - o(i,j)] (l - 6) ^ 

 ay Ay Ay 



(11) 



where ^ is a temporal weighting factor, Ay = y^+i - yi, and At = t^*^ - t J . 



48. The weighting factor 8 determines the type (as explicit or implic- 

 it) and stability of the numerical method, and its value ranges from to 1 . 

 For ^ = 0, the numerical solution scheme is explicit; with 6 = 0.5, the 

 numerical solution scheme becomes implicit centered in time; and 9=1 

 produces a fully implicit scheme forward differenced in time. 



49. If the variables and their derivatives in Equations 6 and 8 are 

 replaced with their equivalent finite-difference representations, then, at 

 each point M contained between sections i and i+1 and time steps J and J+1 , 

 two algebraic equations representing the differential Equations 7 and 8 can be 

 written. 



50. The equation of continuity. Equation 7, is replaced by Equation 12, 

 and the finite-difference representation of the equation of conservation of 

 momentum (Equation 8) is written as Equation 13. 



21 



