Question regarding Maccormack Technique

[Zachary Davis]

I'm somewhat of a beginner/student to CFD development, and I'm making
my way through John D. Anderson's "Computational Fluid Dynamics: The
Basics With Applications" wherein Maccormack's finite differencing
technique is being utilized to solve the flowfield for a quasi-1D,
subsonic inflow-supersonic outflow isentropic nozzle. The governing
flow equations are reduced for a quasi-1D Euler flow, and cast in
strong conservation form. In writing my own program to solve this
problem, I have been able to match Anderson's results for the first
step in time. However, my code becomes unstable as I advance further
in time, and I'm unable to obtain a stable solution using the Courant
number, grid spacing, and time steps that Anderson specifies.

I'm wondering if this may have something to do with my implementation
of calculating the time increment itself, which Anderson is a little
vague in how he himself handles this. I know that for each grid point
the time increment is calculated, and he in turn picks the minimum time
increment calculated across each grid point to advance the solution to
the next time step (global time marching approach). However, I'm left
wondering if this is repeated for each time iteration, or if this
minimum time increment calculated for the first time step is used for
subsequent iterations. I have implemented the former approach, and I
see that as the solution steps forward in time the minimum time
increment calculated across all the grid points diminishes; eventhough,
the grid spacing remains constant. Is this normal, or should the time
increment remain constant while the solution marches in time? Any
insights would be most helpful.

Thanks.

[SK]

I guess this is normal....
I dont know why you are facing so much problem the code is explained
neatly in the book
I have written that code ....
my suggestion try to run only for one time step find the mistakes then
run further...
Since it is 1d solution you can have a sample hand calculation to
correct
in fact i think the result after first time step is also explained...
About CFL you can later modify and run it for each time step that
would improve your code
best luck

[Zachary Davis]

Thanks, as I mentioned my initial condiitons, area distribution, and
results after the first time step match those Anderson provides. I'm
just trying to determine why my solution goes unstable after the same
courant value, mesh spacing, and number of time steps that Anderson
specifies. It appears that I've implemented calculation of the time
step and evaluation of the minimum value across all the grid points
correctly, so I suppose I will need to look elsewhere for the culprit.

[SK]

Have u chked the outlet B.C. ....extrapolation of calculated data
bcoz that is something that might cause garbage entries in ur code....
and since it is 1d code there wont be more than 1 set of corrector-
predictor...
if u want u can send me ur code...i can try wht is goin wrong...hope
it is in c, c++...:)
best luck
sachin