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Two solutions of Sod's shock tube problem

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Old   January 23, 2013, 18:52
Default Two solutions of Sod's shock tube problem
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Orxan Shibliyev
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Hi

When I was googling I found two solutions of the Sod's shock tube problem with the same initial conditions. In the given references, especially density profiles are different. My solution is the same as the second reference. Do you have any idea how there could be two solutions with the same initial conditions? The references are:

1. http://www.csun.edu/~jb715473/exampl...1d.htm#density
2. http://irfu.cea.fr/Projets/Site_hera...est_suite.html
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Old   January 24, 2013, 00:42
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This is strange. I always get the first solution for this problem. This is a standard test case and you can see sample results in most books like Toro which show the first solution. Toro's book also has exact Riemann solution which you use for this problem.
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Old   January 25, 2013, 15:26
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Interestingly I get the first result with my 1D code but I get second one with my 3D code. I cannot figure out why this happens.
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Old   January 30, 2013, 09:27
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This is very strange. I concur that the first solution is the same as the one in Toro and is the result I obtain with my code using 1D or 3D tests.

If the results differs between 1 and 3D solvers is it to do with the storage and/or order of flux splitting?

The second page is very interesting, though I'm somewhat concerned for anyone trying to replicate those results, for a 1D shock tube okay we should be able to do it, but for example the Rayleigh-Taylor case, this result is very dependent on the order of accuracy of the code (and even which implementation e.g MUSCL or WENO etc) so I think while you would reproduce the basic bubble/spike image to get the exact same detail is most unlikely. Liska and Wendroff have a good paper showing it "Comparison of several difference schemes on 1D and 2D test problems for the Euler equations".

Sorry, a bit off topic but I'm keen to hear a solution to the OP's question and reignite some interest in methods :-)

Mike
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Old   January 30, 2013, 16:32
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I tried 2nd order accuracy in space and 4th order in time however that only makes the solution to look sharper and "better". Still my answer is same as the second resource.
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Old   January 30, 2013, 16:35
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Sorry Orxan, my comments weren't really directed at the solution of the Sod problem, rather the other solutions on that page. I was just worried that if the latter data was a bit misleading the former could be too.

Certainly I wouldn't expect the order of accuracy to effect the Sod solution very much (definitely not in the manner here). This second solution is a mystery to me and I am eager to find the answer!

Mike
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Old   January 31, 2013, 00:51
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Are the 3-d simulations in cartesian or spherical coordinates ? Perhaps the 3d simulations are obtaining radial solutions which would be different from plane shock tube solutions.
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Old   February 2, 2013, 07:45
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are there any experimental results?
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Old   February 2, 2013, 09:51
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the diagrams is told that are in t=.1s but it seems too much time and at this time equilibrium is almost reached.what time should be set accurately?
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Old   July 7, 2013, 06:40
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hi,
ı want to make difference of pressure to be shock but ı don how to do this, so can you help me ?
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Old   February 6, 2014, 11:21
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is there any data about after reflection of shock from the wall? (pressure,density,temperature)
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Old   November 12, 2014, 04:48
Default Instability in solution
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Hi all,

I am trying to simulate sod's shock tube with Mccormack scheme (second order). I am getting infinite values, and solution becomes unstable very soon. Anyone has any idea what is going wrong.
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Old   May 20, 2016, 20:51
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Quote:
Originally Posted by gaurav11 View Post
Hi all,

I am trying to simulate sod's shock tube with Mccormack scheme (second order). I am getting infinite values, and solution becomes unstable very soon. Anyone has any idea what is going wrong.
Hey did you ever find the solution to this?

If so, can I see your code?
I am having the same issue and it is driving me crazy.
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Old   May 20, 2016, 21:32
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Quote:
Originally Posted by gaurav11 View Post
Hi all,

I am trying to simulate sod's shock tube with Mccormack scheme (second order). I am getting infinite values, and solution becomes unstable very soon. Anyone has any idea what is going wrong.
Please give more details. Based on my previous experiences, maybe:
1. CFL is too large.
2. Incorrect way to compute flux.
3. inappropriate boundary condition.
4. simple mistake: for example , take "i" as j".

If you code blows very soon, there must be some fatal errors. I suggest you deal with the simple case first. Give an artificial initial conditions, say let density be a linear function in the whole computational domain. Debug step by step, see what you can dig.
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Old   May 20, 2016, 21:41
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Quote:
Originally Posted by AeroMike View Post
This is very strange. I concur that the first solution is the same as the one in Toro and is the result I obtain with my code using 1D or 3D tests.

If the results differs between 1 and 3D solvers is it to do with the storage and/or order of flux splitting?

The second page is very interesting, though I'm somewhat concerned for anyone trying to replicate those results, for a 1D shock tube okay we should be able to do it, but for example the Rayleigh-Taylor case, this result is very dependent on the order of accuracy of the code (and even which implementation e.g MUSCL or WENO etc) so I think while you would reproduce the basic bubble/spike image to get the exact same detail is most unlikely. Liska and Wendroff have a good paper showing it "Comparison of several difference schemes on 1D and 2D test problems for the Euler equations".

Sorry, a bit off topic but I'm keen to hear a solution to the OP's question and reignite some interest in methods :-)

Mike
Hello, Mike
I would like to ask if you have any experiences dealing discontinuities with minmod limiters. I got some problems with my code for 1D shock nozzle. I can get a convergent solution without limiters. But Lax-Wendroff oscillations occur at the discontinuity. Unfortunately, my code blows after adding a minmod limiter.
By the way, I am trying a high-order method named Correction Procedure via Reconstruction (CPR). Finite Volume method coincides well with the exact solution.
Good luck.
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