# Numerical Scheme for a CFD problem

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 September 22, 2013, 17:34 Numerical Scheme for a CFD problem #1 New Member   Join Date: Sep 2013 Posts: 6 Rep Power: 3 Hi, I am quite new to the CFD field and I am eager to learn. In particular, I am trying to write down a code from scratch in order to solve a CFD problem, but I am not sure which numerical scheme is better for my purposes (I don't want to use a ready-to-use CFD package). In particular, my problem has the following features: 1) Spherical symmetry 2) Time dependent 3) Supersonic regime 4) No viscosity 5) Optically thick medium 6) No chemical reactions and no magnetic fields At the moment I don't need a super-accurate numerical scheme, just something to start with which is sufficiently precise. Thank you very much for any help. Marco

September 23, 2013, 04:02
#2
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Filippo Maria Denaro
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Quote:
 Originally Posted by Saturn_V Hi, I am quite new to the CFD field and I am eager to learn. In particular, I am trying to write down a code from scratch in order to solve a CFD problem, but I am not sure which numerical scheme is better for my purposes (I don't want to use a ready-to-use CFD package). In particular, my problem has the following features: 1) Spherical symmetry 2) Time dependent 3) Supersonic regime 4) No viscosity 5) Optically thick medium 6) No chemical reactions and no magnetic fields At the moment I don't need a super-accurate numerical scheme, just something to start with which is sufficiently precise. Thank you very much for any help. Marco

Hello, if I am write, you need to solve a 1D problem (t,r)?
Therefore, standar solvers for Euler equations are suitable for you (see the book of LeVeque or the older book of Hirsch). You can start by developing a simple first-order scheme, that is forward time integration plus first-order upwinded flux reconstruction.
That is simple to code but is quite diffusive therefore I suggest to use a very refined grid.
What do you mean for "Optically thick medium"?

 September 23, 2013, 11:16 #3 New Member   Join Date: Sep 2013 Posts: 6 Rep Power: 3 Yes, I need to solve a 1-D problem (r,t). By optically thick I mean that the medium (gas) absorbs and re-emits radiation in an extensive manner. So maybe I could use a simple Godunov's solver ? Thank you Marco

September 23, 2013, 12:12
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Filippo Maria Denaro
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Quote:
 Originally Posted by Saturn_V Yes, I need to solve a 1-D problem (r,t). By optically thick I mean that the medium (gas) absorbs and re-emits radiation in an extensive manner. So maybe I could use a simple Godunov's solver ? Thank you Marco

yes, with a very fine grid

September 24, 2013, 12:35
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I have implemented a basic Godunov solver and I am testing it with the Sod shock tube test.
I am attaching the plot of the velocity as a function of the position (the initial discontinuity is a x=0.3). As you see, the graph is quite good, but there is a strange increase in velocity around the shock front position.
I do suppose that this is a numerical issue due to the elementary method I used. Maybe more advanced methods could represent the shock front in a much better way. Do you think that this is the case?
If so, this method is good for me because for my application i do not expect to encounter strong discontinuities.

Thank you very much for all the cooperation!

Marco
Attached Files
 Sod.pdf (9.1 KB, 12 views)

 September 24, 2013, 13:07 #6 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 1,588 Rep Power: 20 you should have an expansion wave region... what about density and pressure? Check this report http://oai.cwi.nl/oai/asset/10964/10964D.pdf

September 24, 2013, 13:15
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Attached you can find density and pressure.

Marco
Attached Files
 density.pdf (14.2 KB, 7 views) pressure.pdf (10.6 KB, 5 views)

September 24, 2013, 13:45
#8
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Filippo Maria Denaro
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Quote:
 Originally Posted by Saturn_V Attached you can find density and pressure. Marco

Your results have some strange behavior ... better you check for the shock tube test in the report, you should have expansion waves, shock and a contact discontinuity ...

 September 25, 2013, 02:54 #9 New Member   Join Date: Sep 2013 Posts: 6 Rep Power: 3 Ok thank you very much for your help. I solved the problem with the Godunov upwind scheme and also coded successfully a HLLC version of the HD integrator, it is fantastic!! Grazie! Marco

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