130
5. Finite Element Methods for Solving Hydrodynamic Dispersion Equations
and
1
(Xa = 8(1 - e)(1 - '1)(1 + (),
thus,
(2) For node i located at amidpoint of a edge, we define
(5.3.18)
when el = ± 1, ' 11 = 0, CI = ± 1;
when el = ± 1, ' 11 = ± 1, CI = 0.
Node 5 has local coordinates (0, -1, -1) and is an example of this case.
Using the first formula ofEq. (5.1.18), we can find
1
2
rPsR, '1, C) = 4(1 - e )(1 - '1)(1 - C)·
(3) For node i located at one-third of an edge, we define
9
2
64 (1 - e )(1 + geel)(1 + '1'1;)(1 + cel),
1
when el = ±j' ' 11 = ± 1, CI = ± 1
9
64 (1 + eel)(1 - '1 2 )(1 + 9'1'11)(1 + cel),
1
when ):. = + 1, t'I. = +- y. = + 1
'0,
-
0" - 3' '0, -
9
2
64 (1 + eel)(1 + '1'11)(1 - C )(1 + 9cel)'
1
when ):. = + 1 t'I. = + 1 Y. = +-.
1:"
- , ."
- , \:t,
- 3
(5.3.19)