3. 321 δδδ zyx qqqq ++=
q is a vector
t
h
SW
z
q
y
q
x
q
s
zyx
∂
∂
−=−
∂
∂
+
∂
∂
+
∂
∂
Transient mass balance equation:
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4. 0=
∂
∂
+
∂
∂
+
∂
∂
z
q
y
q
x
q zyx
The dot product of
grad and q is
div q = 0
grad • q = 0
Steady State Mass Balance Equation with W = 0
∇ • q = 0 (del notation)
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6. Homogeneous, isotropic Homogeneous, anisotropic
A A
B B
Heterogeneous, isotropic Heterogeneous, anisotropic
A
A
B
B
Characteristics of K in two dimensions
Kz
Kx
Kx ≠ Kz
••
Kx = Kz = K
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7. Homogeneous, isotropic Homogeneous, anisotropic
A A
B B
Heterogeneous, isotropic Heterogeneous, anisotropic
A
A
B
B
Characteristics of K in two dimensions
Kz
Kx
Kx ≠ Kz
••
Kx = Kz = K
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9. Tot h Pr ob le m ( 2 D)
Impermeable Rock
Groundwater
divide
Groundwater
divide
2 D, st e ad y st at e
02
2
2
2
=
∂
∂
+
∂
∂
z
h
x
h
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10. i, j
j
i
The 5 point star
in a regular grid
i+1, ji-1, j
i, j-1
i, j+1
∆x
∆y
∆x = ∆y
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11. 04 ,1,1,,1,1 =−+++ −+−+ jijijijiji hhhhh
4
1
1,1,
1
,1,11
,
+
−+
+
−++ +++
=
m
ji
m
ji
m
ji
m
jim
ji
hhhh
h
Solution by iteration
Gauss-Seidel Iteration
4/)( 1,1,,1,1, −+−+ +++= jijijijiji hhhhh
Iteration indices
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