x-t diagram
matei
the evolution of a gasdynamic problem? Say obtain a contour plot of
any of the gasdynamic variables on an x-t diagram? If so, has anybody
ever integrated the path of the three families of characteristics?
I would like to use such solutions in a gasdynamic course i teach, and
for my own research.
On a related topic, is it possible to output the solution at fixed
time increments, rather than being constrained by the time steps
imposed by the CFL condition?
Thanks,
matei
James Quirk
On Wed, 29 Oct 2008, matei wrote:
>
> Has anyone ever implemented a script to construct an x-t diagram of
> the evolution of a gasdynamic problem? Say obtain a contour plot of
> any of the gasdynamic variables on an x-t diagram? If so, has anybody
> ever integrated the path of the three families of characteristics?
I rememember helping Hans to produce a x-t diagram but I don't
have the script to hand. It basically involded using the translate
command to plot a stack of 1d slices. When I get the chance I'll
put together an example that shows the basic approach.
>
> I would like to use such solutions in a gasdynamic course i teach, and
> for my own research.
>
> On a related topic, is it possible to output the solution at fixed
> time increments, rather than being constrained by the time steps
> imposed by the CFL condition?
Yes. Launch amrhelp and checkout amr_sol::march it has a variant
of the form:
march to t=$t with dt=$dt
James
>
> Thanks,
> matei
James Quirk
>
> Matei,
>
> On Wed, 29 Oct 2008, matei wrote:
>
> >
> > Has anyone ever implemented a script to construct an x-t diagram of
> > the evolution of a gasdynamic problem? Say obtain a contour plot of
> > any of the gasdynamic variables on an x-t diagram? If so, has anybody
> > ever integrated the path of the three families of characteristics?
> I rememember helping Hans to produce a x-t diagram but I don't
> have the script to hand. It basically involded using the translate
> command to plot a stack of 1d slices. When I get the chance I'll
> put together an example that shows the basic approach.
I whipped up a quick script that plots an xt diagram for
sod's shock-tube problem w with reflectibg boundary conditions
on the left and right ends of the domain. The script shows the
approach to take, but it is left as "an exercise for the reader"
to produce a resuable procedure.
James
matei
thanks, I'll have a go at it.
In your opinion, what would be the best way to extract the
characteristic families? I can add some equations and just integrate
explicitly the new position of the characteristic location, or do it
in post-processing?
matei
> 2KViewDownload
James Quirk
It's difficult to answer yout question without knowing
what end result you want to achieve. Can you elaborate?
James
matei
What I would like to do is the following. Say I compute a 1-
dimensional unsteady problem like a pulsating detonation. I would like
to display the path of the C+, C- and Co characteristics starting at
fixed locations that I choose. For example, i want to follow the path
x(t,xref) where xref is the position at t=tref, according to the
characteristic directions dx/dt=u+c, dx/dt=u-c and dx/dt=u.
I could do the integration quite easily explicitly in post-
processing. Say i know the solution at t=t1, i can find the new
positions explicitly by a first order approximation.
The idea is the same as setting lagrangian trackers, only now there
are two extra trackers, one along the C+ characteristics, the other
along the C- characteristics.
The reason why I would need this is to better visualize the dynamics
in pulsating detonations, and other non-steady gasdynamic problems.
Eventually, i would like to extend it to 2D, in order to visualize the
dynamics of waves and permit to better visualize compression waves,
expansion waves, etc... in order to reconstruct the physics of
unsteady compressible flows.
This could be time-consuming in post-processing, so it would be better
to automate it within AMRITA for reproducibility purposes. Doing it
explicitly would be the easiest way, but I guess one can implement a
higher order integration of these paths.
For the detonation problem (propagating towards the x>0 axis
direction, say), I would like to plot a family of C+'s originating in
the detonation reaction zone, say along a fixed t line. These lines
eventually reach the shock and reflect back along C- and give rise to
changes along Co's. For the Co and C-, I want to integrate the paths
of these lines originating from x,t points along the path of the
leading shock, and follow them as they propagate towards the products
region downstream.
I can send you a sketch, if that helps.
matei
James Quirk
On Fri, 31 Oct 2008, matei wrote:
>
> James,
> What I would like to do is the following. Say I compute a 1-
> dimensional unsteady problem like a pulsating detonation. I would like
> to display the path of the C+, C- and Co characteristics starting at
> fixed locations that I choose. For example, i want to follow the path
> x(t,xref) where xref is the position at t=tref, according to the
> characteristic directions dx/dt=u+c, dx/dt=u-c and dx/dt=u.
> I could do the integration quite easily explicitly in post-
> processing. Say i know the solution at t=t1, i can find the new
> positions explicitly by a first order approximation.
The situation is not quite as easy as you might suppose
in that you will have to contend with a computational grid
that is changing dynamically, which means that the required book-keeping
is somewhat fiddly.
>
> The idea is the same as setting lagrangian trackers, only now there
> are two extra trackers, one along the C+ characteristics, the other
> along the C- characteristics.
>
> The reason why I would need this is to better visualize the dynamics
> in pulsating detonations, and other non-steady gasdynamic problems.
> Eventually, i would like to extend it to 2D, in order to visualize the
> dynamics of waves and permit to better visualize compression waves,
> expansion waves, etc... in order to reconstruct the physics of
> unsteady compressible flows.
I understand your motivation. In the past I have simulated the
firing of a laser so as to generate an acoustic pulse whose
propagation front can then be monitored. This was done
to check Takayama's thesis regarding the transition of
RR to MR, and if you take a look at the ramp mailit from
the vki notes, you'll see a FireLaser procedure.
Obviously in a reactive flow this approach is not
very useful in that it would likely trigger preamture reaction.
>
> This could be time-consuming in post-processing, so it would be better
> to automate it within AMRITA for reproducibility purposes. Doing it
> explicitly would be the easiest way, but I guess one can implement a
> higher order integration of these paths.
The automaion would be done inside of amr_sol, which lives inside
amrita. And the time-consuming part will be constructing a general
purpose approach rather than a kludge for a one-off problem.
The work is tractable in 1D but in 2D I'm not so hopeful
as it would be like adding a front tracking program. Of course
much depends on what you want the front propagation for
i.e. can you get away with something that is qualitative
rather than quantitative.
>
> For the detonation problem (propagating towards the x>0 axis
> direction, say), I would like to plot a family of C+'s originating in
> the detonation reaction zone, say along a fixed t line. These lines
> eventually reach the shock and reflect back along C- and give rise to
> changes along Co's. For the Co and C-, I want to integrate the paths
> of these lines originating from x,t points along the path of the
> leading shock, and follow them as they propagate towards the products
> region downstream.
>
> I can send you a sketch, if that helps.
No need. I understand what you would like, but I'm afraid
that work involved is harder than it first looks.
James