Numerical Scheme for a CFD problem
 

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"?

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 ;)

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

you should have an expansion wave region... what about density and pressure?

Check this report http://oai.cwi.nl/oai/asset/10964/10964D.pdf

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 ...

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