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September 22, 2013, 17:34 
Numerical Scheme for a CFD problem

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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 readytouse 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 superaccurate 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:
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 firstorder scheme, that is forward time integration plus firstorder 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 

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Yes, I need to solve a 1D problem (r,t).
By optically thick I mean that the medium (gas) absorbs and reemits 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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September 24, 2013, 12:35 

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Thank you very much for your reply.
I have implemented a basic Godunov solver and I am testing it with the Sod shock tube test. I just want to ask an additional information. 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 

September 24, 2013, 13:07 

#6 
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Filippo Maria Denaro
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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 

September 24, 2013, 13:45 

#8 
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Filippo Maria Denaro
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September 25, 2013, 02:54 

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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 

Tags 
numerical methods, numerical scheme, numerical simulation, physical model 
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