APPENDIX A
Alternating Direction Implicit Finite Differencing
An alternating direction implicit solution method was developed to
solve the two-dimensional radial flow model. The solution method
divides the solution into two half cycles, thus two cycles are required
to solve for one time step. Equation (8) was solved in the radial
direction during the first half cycle and then solved in the vertical
direction during the second half cycle. The ADI solution for equation
(8) may be written as
k+1/2
k+1/2
k+1/2
k+1/2 8 h
1
1 3 k+1/2 3 h
1 3 k+1/2 3 h
C =
- (
(r K _
) + (r K
) )
3 t
r
2 3r 3 r
2 3 r
3 r
k+1
k
13 k+1 3 h
13 k 3 h
+
(
(K )
+ (K _)
)
2 3 Z 3 Z
2 3 Z 3 Z
k+1/2
k+1 k
1 3 K 1
3 K 3 K
+
(
+ (
+ )
- S(z,r,t)
2 3 z 4
3 Z 3 Z
(68)
The finite difference equations used for the solution of equation (8)
were expressed as
k+1 k
(h h )
i,j i,J
C
i,j
At
(69)
126