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

#1 
New Member
Join Date: Sep 2013
Posts: 6
Rep Power: 4 
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  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,003
Rep Power: 27 
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 

#3 
New Member
Join Date: Sep 2013
Posts: 6
Rep Power: 4 
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 

#4 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,003
Rep Power: 27 

September 24, 2013, 12:35 

#5 
New Member
Join Date: Sep 2013
Posts: 6
Rep Power: 4 
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 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,003
Rep Power: 27 
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 

#7 
New Member
Join Date: Sep 2013
Posts: 6
Rep Power: 4 
Attached you can find density and pressure.
Marco 

September 24, 2013, 13:45 

#8 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,003
Rep Power: 27 

September 25, 2013, 02:54 

#9 
New Member
Join Date: Sep 2013
Posts: 6
Rep Power: 4 
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 
Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Future CFD Research  Jas  Main CFD Forum  10  March 30, 2013 13:26 
What a CFD scheme means?  Accelerator  Main CFD Forum  0  March 28, 2012 04:02 
CFD problem setup for flow through porous media  Paresh Jain  CFX  5  June 30, 2003 03:50 
ASME CFD Symposium  Call for Papers  Chris Kleijn  Main CFD Forum  0  September 25, 2001 10:17 
PC vs. Workstation  Tim Franke  Main CFD Forum  5  September 29, 1999 15:01 