Mean flow:
(
)
o
j
o
o
o
io
jo
io
j
o
i
io
t
x
v
v
t
v
v
x
p
x
F
+
=
+
÷
+
=
0
Acoustic perturbation:
t
v
x
v
x
q
jo
j
o
j
j
+
+
=
o
i
jo
i
j
i
i
v
t
v
v
x
p
x
f
+
÷
÷
+
=
CAA
0
,
v
j0
Time-averaged
corrections to
F
i
0
n
e
w
s
p
u
W
E
n
s
v
N
S
e
w
56 time steps, Courant number = 0.7
Plane Wave (1D test case)
-20
0
20
40
60
80
100
6
8
10
12
14
16
Distance from source
Acoustic pressure
computed
exact
error
Spherical Wave
-30
-20
-10
0
10
20
30
40
50
0
2
4
6
8
10
12
Radial Distance
Acoustic Pressure
p1
exact_1
p2
exact_2
p3
exact_3
symmetry axis
radial axis
p3
p2
p1
point source
Courant number = 0.7 = limit in 2D
-20
0
20
40
60
80
100
120
460
465
470
475
480
Distance along axis of propagation [m]
Acoustic pressure [Pa]
computed
exact
error
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