1
Oct. 17, 2006
ATMS 502  CS 505  CSE 566
Jewett
Computer Problem 4
2D Advection: Rotational and Deformational Flow
Due
: Tuesday, October 31.
Turn in
: your code (printed out, and
also
emailed to me), and plotted results (on paper).
Problem being solved:
2D advection with fractional step (directional) splitting.
Boundary condition:
0gradient (extrapolation outward, whether inflow
or
outflow)
Evaluation:
You will compute error statistics for the one case (rotational flow) with a
known solution, following Takacs (1985, eqn. 6.16.7), evaluated over the 2D domain.
Methods:
Crowley (Tremback et al.,
Mon. Wea. Rev.
, 1987), 2
nd
and 6
th
order.
1. Crowley 2
nd
order
(same as LaxWendroff)
"
j
n
+
1
=
"
j
n
+
#
2
"
j
$
1
n
$
"
j
+
1
n
(
)
+
#
2
2
"
j
+
1
n
$
2
"
j
n
+
"
j
$
1
n
(
)
2. Crowley 6
th
order
See Tremback p. 542, ORD=6 (advective form)
For all of the above,
"
=
#
t
#
x
•
local
u
or
v
(
)
(i.e. it is the local Courant number)
Domain:
The computational domain is a twodimensional staggered Cgrid, with the
scalar field
q
stored over a 101x101 domain, with
∆
x=
∆
y=
1
nx
"
1
#
$
%
&
’
(
. The physical
coordinates
for
q
range from 0.5 to +0.5 in each direction. The
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 Spring '09
 JEWETT
 Boundary value problem, Boundary conditions, deformational flow, rotational flow

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