CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Chebyshev Polynomials in a infinite Channel???

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   April 4, 2002, 17:07
Default Chebyshev Polynomials in a infinite Channel???
  #1
Carlos
Guest
 
Posts: n/a
Hi, I have to work numerically in a channel, but without streamwise periodic conditions ( non-established regime), and a priori unbounded. Is it possible to use Chebyshev's Polynomials for it, and, if one can, how? (Up to here, I had thought to imposing some lenght for the channel and map it into the interval [-1,1], but that seems to me excesive as approach, since a priori I dont know the lenght necessary for the analysis). Thanks in advance,
  Reply With Quote

Old   April 5, 2002, 07:57
Default Re: Chebyshev Polynomials in a infinite Channel???
  #2
Paul
Guest
 
Posts: n/a
No matter whether you know the domain length a priori or not, you must choose one for your computation. Generally, you can choose a length which seems large enough based on your knowledge on the flow field and based on the different types of flow. An appropriate length should be that whose enlargment should not change the numerical result.

-Paul
  Reply With Quote

Old   April 5, 2002, 10:34
Default Re: Chebyshev Polynomials in a infinite Channel???
  #3
Patrick Godon
Guest
 
Posts: n/a
And you will need to impose the boundary conditions properlly, because the chebyshev method is very sensitive to wrong boundary conditions. You will have to impose the BC on the 'invariants' of the flow, see for example treatment on non-reflective BC. ALso since your channel is 'infinite', it means that waves can actually 'escape' to infinity, i.e. not be reflected at the boundary.
  Reply With Quote

Old   April 6, 2002, 10:35
Default Re: Chebyshev Polynomials in a infinite Channel???
  #4
peter
Guest
 
Posts: n/a
For propblems with viscosity on an infinite domain it may be best to first try a spectral method with polynomials that are localized, i.e., polynomials that satisfy the fact that long away from the domain of interest the viscosity will damp everything to zero (or pretty close to it).

Peter
  Reply With Quote

Old   April 8, 2002, 10:48
Default Chebyshev Polynomials in a infinite Channel???
  #5
Carlos
Guest
 
Posts: n/a
Thank you very much for all your suggestions.

I am going to try with the first suggestion (to fix a lenght a priori).

Concerning the second answer (suitable BC, the condition of zero normal derivative; or "do nothing" BC, is this one a "good" condition?

Finally, the use of the localized polynomyals seems interesting. Can You give me some bibliographical references?

Thank you once again

Carlos
  Reply With Quote

Old   April 9, 2002, 15:05
Default Re: Chebyshev Polynomials in a infinite Channel???
  #6
Patrick Godon
Guest
 
Posts: n/a
There are two things that you need to consider when imposing the BC. First what are the 'physical' BC you want to impose, in this case you mean for example zero derivative (I am not sure what you mean by do nothing BC). The best is to impose kind of fixed BC, BC that are not a results of the simulations themselves. The second stage is that you imposed these conditions on the variables through the characteristics of the flow, in 1D the characteristics are the Rieman invariants. It would be very long to explain all that here, the best would be to look at some paper on non-reflective BC for example. Or look at the details on the imposition of BC in spectral methods (in books or in some papers in a journal).

For non reflective BC, see for example:

Givoli, D., 1991, Journal of Computational PHysics, volume 94, page 1.

For treatment and imposition of BC in spectral methods, see for example:

Abarbanel et al. 1991, Journal of Fluid Mechanics, 225, 557.

Gottlieb, Gunzburger, Turkel, 1982, SIAM J. Numer. Anal. 19, 671.

You might also want to have a look at the book:

Spectral Methods for partial differential equations, SIAM-CBMS, 1984, by Voigt, Gottlieb, Hussaini (Philadelphia, PA).
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Open Channel Flow ElanMorin FLUENT 4 February 25, 2015 17:26
Open channel flow motaba Main CFD Forum 4 March 26, 2011 04:22
tecplot 3D velocity contours inside a channel vetnav Tecplot 4 July 14, 2010 20:03
About Cooling channel alefem FLOW-3D 1 May 28, 2010 11:15
Open Channel Boundary Conditions via journal Matteo FLUENT 0 January 21, 2008 12:05


All times are GMT -4. The time now is 04:36.