Computational Fluid Dynamics
Lecture 19
We will examine open boundary conditions of 5 types.
1.
Constant advection with one way wave equation with
c
*
2
=
and 3.
2. Zero gradient condition
3. Rayleigh damping region with:
a. 10 grid points
b. 20 grid points
c. 100 grid points
4. Orlanski equation
5.
Time averaged Orlanski method with a time average of 1s.
The test problem is Burgers equation on the intervals
0
x
10
<
<
with an open boundary at
( )
10
x
x
L
=
=
0
30
x
<
<
and the reference “exact” solution is the same problem solved on the interval
.
Burgers equation is”
(
)
( )
( )
(
)
( )
2
2
suggested initial conditions are
2
,0
2
sin
on the interval 0
and
,0
2 for
.
x
x
x
u
u
u
u
v
t
x
x
x
u x
L
x
L
u x
x
L
π
∂
∂
∂
+
=
∂
∂
∂
=
+
<
<
=
>
An appropriate small value of
v
should be determined by experimentation such that it is large
enough that the propagating wave does not “break” during the simulation.
The boundary condition
at
(
)
(
0 is
0,
2
sin
)
x
u
t
ct
=
=
+
(
)
−
where we are considering a linear wave propagating into the domain
( )
2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Slinn
 Partial Differential Equations, Boundary value problem, Computational fluid dynamics, Boundary conditions

Click to edit the document details