276 Computational Modelling in Hydraulic and Coastal Engineering
The analytic expression for each of the constant coefficients is given as
follows (Scarlatos 1982):
α 1 1
1
2
6 2 2
2
,
(
)
= −
+
+
u u
t
x
S e
∆
∆
(9.85)
α 1 2
6
, = − g
t
x
∆
∆
(9.86)
α 1 3
1
2
3 2 2
,
(
)
= +
+
+
u u
t
x
S e
∆
∆
(9.87)
α 1 4 6
, = g
t
x
∆
∆
(9.88)
α
λ
λ
ζ
λ
ζ
2 1
1
2
6
4
4
2
,
(
)
(
)
= − +
+
+
−
+
−

 

 




h h
S x
x
x
o ∆
∆
∆
 

∆
∆
t
x
(9.89)
α 2 2
1
2
2 3 2
,
(
)
=
−
+






u u
t
x
∆
∆
(9.90)
α
λ
λ
ζ
λ
2 3
1
6
1
2
4
4
4
2
,
(
)
=
+
+
+
+

 

  +
+

 

 
h
h
S x
x
x
o ∆
∆
∆
ζ ζ 2






∆
∆
t
x
(9.91)
α 2 4
1
2
3 2 2
,
(
)
= +
+
u u
t
x
∆
∆
(9.92)
α 3 1
1
2
3 2 2
,
(
)
= −
+
+
u u
t
x
S e
∆
∆
(9.93)
α 3 2
6
, = − g
t
x
∆
∆
(9.94)