129
1
- ( -
2
k
At K
i+1/2,j k+1
) h
2 i+l,j
Az C
ij
1 At
+ __ (
4 Az
k+1/2 k+1/2
K k
t-1/2, j i+1/2, j
)
C
i,j
1 A t
2 C
i.j
k
S
i,j
k+1/2
1
At r
i.j-1/2
K
i.j-1/2
2
2
A r r
C
i.j
i.j
1
At r
k+1/2
K
i.j+1/2
i.j+1/2
2
2 Ar r C
i.j i
k+1/2 k+1/2
h h )
i.j-1 i.J
k+1/2 k+1/2
h h ) (74)
i.j+1 i.j
where i represents the vertical distance, j represents the radial
distance and k represents the time increment.
The system of equations which are formed by applying equations (73)
and (74) to each grid point produces a tridiagonal matrix at each half
time step. The tridiagonal matrices were solved using a Gauss
elimination method for tridiagonal matrices. Equations (73) and (74)
may be simplified such that equation (73) may be written as
k+1/2 k+1/2 k+1/2
- AR h + BR h CR h = DR
i.j-1 i.j i.j+l i.j
(75)