2.3 Implementation of Numerical Solution
35
Fig. 2.6 Staggered grid
ρv
∗
n+1
i, j+1/2
=
ρv
∗
n
i, j+1/2
+ B
∗
t −
t
y
p
∗
i, j+1 − p
∗
i, j
(2.48)
where
A = −
ρu
2
n
i+3/2, j
−
ρu
2
n
i−1/2, j
2x
+
(ρuv)
n
i+1/2, j+1 − (ρuv)
n
i+1/2, j−1
2y
+ μ
u
n
i+3/2, j − 2u
n
i+1/2, j + u
n
i−1/2, j
(x)
2
+
u
n
i+1/2, j+1 − 2u
n
i+1/2, j + u
n
i+1/2, j−1
(y)
2
B = −
ρv
2
n
i, j+3/2
−
ρv
2
n
i, j−1/2
2y
+
(ρuv)
n
i+1, j+1/2 − (ρuv)
n
i−1, j+1/2
2x
+ μ
v
n
i+1, j+1/2 − 2v
n
i, j+1/2 + v
n
i−1, j+1/2
(x)
2
+
v
n
i, j+3/2 − 2v
n
i, j+1/2 + v
n
i, j−1/2
(y)
2