WAVELENGTH
M
4&
3&
2lt.
........
SO&
1l1&
IOd
.
. E
31l14&
...
.'
W
::J
0
W
a:
u. ll12lt.
cn
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<
o
.;,'
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2"\
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... ... . .
- - - ..... 4, ...
1l14&
>U
Z
0
0
1l14&
ll12lt.
31l14&
ll1li
WAVE NUMBER
FIGURE 2.9. Scaled frequency (w ie) as a function of wave number for the analytic solution of the advection equation (dotted line) and for corresponding differential-difference
approximat ions using second- (solid line) and fourth-order (dashed line) centered differences.
SOli
WAVELENGTH
4li
IOli
=".::. .
L -
ll12lt.
WAVE NUMBER
----'--1l14li
-
ol-Jl-o
c
w
w
cn
Cl.
cn
w
< J:
o
Cl.
- - ' -
31l14li
2
3li
E
.
- ' - - '
FIGURE 2.10. Phase speed as a function of numerical resolution for the analytic solution of the advection equation (dotted line) and for corresponding differential-difference
approx imations using second- (solid line) and fourth-order (dashed line) centered differences .