# Time-marching scheme diverges

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 October 12, 2013, 16:42 #21 Member     Serge A. Suchkov Join Date: Oct 2011 Location: Moscow, Russia Posts: 74 Blog Entries: 5 Rep Power: 7 1) In your case outlet BC should be d[rho,U,V,h]/dx=0 2) Negative values ​​of pressure, temperature and density suggest that your solution is unstable, In this case for chosen numerical method I would suggest to reduce the time step or CFL ...or use more recent numerical methods. PS: extrapolation is bad way, because in this case you are replacing the physical laws of conservation of computational tricks __________________ OpenHyperFLOW2D Project

 October 12, 2013, 17:02 #22 Member   Obad Join Date: Sep 2013 Posts: 36 Rep Power: 5 Hy, alright, then I will try it with zero gradient instead of extrapolation. Does the reduction of the CFL really make the code much more stable. I understand the reason for CFL and of course it should not be to big and in my case I see that I definitely shouldn't choose Courant numbers above 0.1. But I mean, is there a certain point where the code becomes stable? Another question is, how does the spacing of the grid influence the stability? My grid has a uniform spacing in x and y direction of about 5mm. Is that small enough? Or does the overall size of the domain influence the stability. As I already stated, I use the Maccormack technique because it is pretty simple. In the 1970s they calculated stuff like the space shuttle with that, so why shouldn't it work in 2013. But maybe you could tell me some other easy to program more modern techniques. Maybe I'll give it a try I really appreciate your help SergeAS!

 October 12, 2013, 17:41 #23 Member     Serge A. Suchkov Join Date: Oct 2011 Location: Moscow, Russia Posts: 74 Blog Entries: 5 Rep Power: 7 The grid spacing will influence the stability in terms of how much will interact different BC. For example in the problems of supersonic aerodynamics bow shock wave can interact with the inlet boundary, moreover mesh size affects the resolution accuracy shocks. As to the Courant number should be noted that it is calculated on the basis of the conditions of linear stability, while the problem with the shock waves are very nonlinear. If we talk about the McCormack method, then it has both pluses and minuses. The most significant downside I just would like to mention a strong dispersion error in the high-gradient area and hence stability problems in these areas. Personally, I do not use the McCormack method for about 15 years. __________________ OpenHyperFLOW2D Project

 October 20, 2013, 18:14 #24 Member   Obad Join Date: Sep 2013 Posts: 36 Rep Power: 5 Ok SergeAS you convinced me. I will try it with a different technique. Although my current code might work properly, I can't really check it because the calculation would take days... Something is confusing me, I read a little bit about the modern shock capturing methods and they are always applied to equations that are discretized with the finite volume technique. Is it necessary in my case to use the finite volume discretization? My geometry is simple and I of course use a structured grid for it. Is there also a modern shock capturing technique that can be used with a finite difference discretization? Could someone suggest me a good technique for unsteady hyperbolic PDEs? Cheers!

October 21, 2013, 03:43
#25
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Filippo Maria Denaro
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Quote:
 Originally Posted by Obad Ok SergeAS you convinced me. I will try it with a different technique. Although my current code might work properly, I can't really check it because the calculation would take days... Something is confusing me, I read a little bit about the modern shock capturing methods and they are always applied to equations that are discretized with the finite volume technique. Is it necessary in my case to use the finite volume discretization? My geometry is simple and I of course use a structured grid for it. Is there also a modern shock capturing technique that can be used with a finite difference discretization? Could someone suggest me a good technique for unsteady hyperbolic PDEs? Cheers!
FV discretizations starts from the weak form of the hyperbolic equations, for this reason they are used in presence of non-regular solutions (shock).
Try a reading to the book of LeVeque

October 21, 2013, 17:06
#26
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Which book do you mean the book Numerical Methods for Conservation Laws?

What does weak form of the equations mean?

For the FDM I used the Euler equations in strong conservation form (this is how Anderson calls them).
Can't I just discretize this equation with the FVM for example by using a second order upwind scheme?
I enclosed how I would discretize the Euler equation in strong conservation form. Would this discretization be correct and could I solve it simply explicitly for every node?
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 October 21, 2013, 18:27 #27 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 2,596 Rep Power: 32 have a reading of http://books.google.it/books/about/F...UC&redir_esc=y

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