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

A question about FDM in cylindrical coordinates.

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

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   November 10, 2004, 14:43
Default A question about FDM in cylindrical coordinates.
  #1
Demidov
Guest
 
Posts: n/a
Hello everybody!

My question is about solving equations (for example Laplass or Poisson equations) in cylindrical coordinates using the finite difference method.

Actually I dont understand which boundary conditions should I apply for this finite-difference scheme in the point r=0 (or r = "very small dr", one dr step for example).

In the point r=R I use (for example) F(r,fi) = 0; In fi=0 and fi= 2pi I use F(r,0) = F(r,2pi); These are the 3 of 4 sides of the corresponding rectangualar.

But which boundary condition should i write for the point r=0 (or r=dr) ? May be, F(0,fi) = F(o,fi+pi)? Or F(0,fi) = F(0, any fi)?

Please, share your experience.
  Reply With Quote

Old   November 10, 2004, 16:56
Default Re: A question about FDM in cylindrical coordinate
  #2
Junseok Kim
Guest
 
Posts: n/a
It depends on how discretize your domain, for example, cell-centered or cell-edged, etc.

  Reply With Quote

Old   November 10, 2004, 17:17
Default Re: A question about FDM in cylindrical coordinate
  #3
Demidov
Guest
 
Posts: n/a
Sorry, can you clarify your answer?

I discretize my domain using the standart 5-point Laplass operator approximation. Without coefficients it is like that: d2F/dr2 = F(r+1,fi) - 2F(r,fi) + F(r-1,fi) dF/dr = F(r+1,fi) - F(r-1,fi) F = F(r,fi) dF/dfi = F(r,fi+1) - 2*F(r,fi) + F(r,fi-1) ... and so on.

So, we have 5-diagonal matrix (except for boundary conditions for fi) with F(r,fi) on the main diagonal.
  Reply With Quote

Old   November 10, 2004, 17:27
Default Re: A question about FDM in cylindrical coordinate
  #4
John
Guest
 
Posts: n/a
See page 67 of this thesis:

http://ctr.stanford.edu/thesis.pdf
  Reply With Quote

Old   November 11, 2004, 05:33
Default Re: A question about FDM in cylindrical coordinate
  #5
Tom
Guest
 
Posts: n/a
Use dF/dR = 0 at r=0.
  Reply With Quote

Old   November 15, 2004, 06:39
Default Re: A question about FDM in cylindrical coordinate
  #6
Salvador
Guest
 
Posts: n/a
See paper by Morinishini et al. (2004) in journal of computational physics (and references there). Remember that the centreleine in a non-physical (grid generated) singularity and special treatment is needed there.
  Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
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 Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Bc in cylindrical coordinates make OpenFOAM Pre-Processing 9 August 8, 2011 07:51
FVM using Cylindrical coordinates RameshK Main CFD Forum 0 December 29, 2009 01:59
RMS velocity in Cylindrical coordinates ? lcw FLUENT 2 October 5, 2006 05:49
O-grids and cylindrical coordinates Satish Perivilli FLUENT 0 May 19, 2005 12:31
comments on FDM, FEM, FVM, SM, SEM, DSEM, BEM kenn Main CFD Forum 2 July 18, 2004 19:28


All times are GMT -4. The time now is 14:08.