A Semi-Implicit, Three-Dimensional Model for Estuarine ... - USGS

76 A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation
t
t
A
n+1
n
n -1
B
n+1
n
n - 1
U i– 1
⁄ 2
n
∂ U
------
∂ x
Δ x
ζ i
Δ x
i 1 2 ⁄ – U ζ i
∂ ζ
------
∂ t
∂ ζ
------
∂ t
U 1
i + ⁄ 2
U
i 1 2 ⁄ +
∂ U
-------
∂ x
∂ U
-------
∂ x
n– 1
n + 1
Δ t
Δ t
Δ t
Δ t
n
∂ U 1
------- = --
∂ x 2
x
( (
∂ U
-------
∂ x
x
n+ 1
∂ U
+ ------
∂ x
Figure 4.4. Computational stencils for (A) explicit leapfrog differencing method and (B) implicit (Crank-
Nicolson type) leapfrog differencing method used in the three-time-level 1-dimensional scheme.
n– 1