Two-dimensional Chebyshev-Fourier DNS software
 

Hi,

I'm currently writing my first DNS-code (FORTRAN or C++) and would appreciate an example of a code to gain insight from. I would like to develope a Chebyshev - Fourier pseudo spectral method to solve incompressible Navier-Stokes in a square or circular domain. Also I intend to use solid boundary conditions!

Any example code or advise would be appreciated. Thanks in advance!

Andy.

Re: Two-dimensional Chebyshev-Fourier DNS software
 

Hi Andy, I can give you a bunch of references on the code that I have been working on for a while and if you like it I can even give you more details on the coding itself. I have used the Chebyshev expansion in the radial direction and the Fourier series in the (periodic) angular direction. Boundary conditions were reflective at the inner boundary and non-reflective at the outer one, but of course there is no problem to implement all that the way you want. THe main paper on that in the Astrophysical litterature: Godon, 1997, The Astrophysical Journal, vol.480, p.329. (if you are at the University of Cambridge there should be no problem to have access to the library of astrophysics). You can have a look there at the 2D code written for a compressible rotating disc. The Chebyshev method is implemented using a method described by Tal-Ezer and Kossloff (1993). Viscousity, filters, external forces are also introduced. Have a look there and tell me what you think. That's a good start. Otherwise I can give you other references for the same kind of hybrid Fourier-Chebyshev solver. So let me know if that's about the kind of code you are looking for and I'll give you more details. Cheers, Patrick.

Channel Flow DNS help request
 

I have just seen some of the related posts. I dont know if you are still interested in the Fourier-Chebyshev topic, but at the moment I am trying to code the same via Matlab.
So far I only have 2d case with three different impementation methods.
1- staggered grid [Canuto-2007]
2- Coupled [Canuto-2007]
3- Splitting method [R.Peyret-Spectral methods for incomp vis flow.]
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with these codes, Couette and Poiseuille flows seem to be working fine. I have two main questions for you;
1-First of all those two cases are fully developed to validate confidently do you have any other suggestion test cases, where solutions are known. There might be many but I would assume, only few would be ok for the periodic B.C.
2-I am pretty confused by stepping up to 3d. I might need some help if you would.
so if you email me back as an answer, I could give you more detailed explanation of the points I get stuck.
emre137@gmail.com
Thanks in advance
\Emre