1
Aug. 29, 2006
ATMS 502  CS 505  CSE 566
Jewett
Computer Problem 1
OneDimensional Linear and Nonlinear Advection
Due
: beginning of class, 2.5 weeks from now: Thursday, September 14.
•
Your code and plots, printed out  handed in
Turn in
:
•
Your code,
emailed
to me w/instructions on how to run it on copper
Problem being solved:
advection equation
Linear case:
"
u
t
=
#
c
u
x
Nonlinear case:
u
t
=
#
u
u
x
The only difference above is use of
c
vs.
u
before
u
/
x
.
Initial condition:
a single sine wave with a wavelength of
nx+1
.
Boundary condition:
periodic; the wave exits the right side of the domain
and reenters the left side (for speed
c
> 0).
Scheme:
LaxWendroff, with forward time, centered space. The form is:
u
j
n
+
1
=
u
j
n
"
#
2
u
j
+
1
n
"
u
j
"
1
n
( )
+
$
u
j
+
1
n
"
2
u
j
n
+
u
j
"
1
n
( )
where
n
is the time level,
j
each of the
nx
grid points,
ν
the Courant number,
and
σ
=
ν
2
/2
.
ν
is set to (c
∆
t/
∆
x) in the linear case, and (u
∆
t/
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 Spring '09
 JEWETT
 Boundary value problem, Boundary conditions, Advection Linear Linear Linear Nonlinear Courant

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