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

singularity problem in cylindrical coordinate

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

Reply
 
LinkBack Thread Tools Display Modes
Old   May 29, 2003, 13:32
Default singularity problem in cylindrical coordinate
  #1
dallybird
Guest
 
Posts: n/a
Hi all,

I've been working on a second-order differential equation using FDM. It is ok when working in Cartesian coordinate. However, in cylindrical system, there is a term '1/r' being introduced, which is singular at r=0. I dont know how to work around it. I know there is some paper talking about Navier-Stokes equations in cylindrical coordinate. But my problem is different in this case.Could anyone suggest some reference book or paper on a general description of solving differetial equations in cylindrical system using FDM? I appreciate that.
  Reply With Quote

Old   May 29, 2003, 13:52
Default Re: singularity problem in cylindrical coordinate
  #2
Praveen
Guest
 
Posts: n/a
See <a href=http://www.flatface.net/~praveen/refs.html>this</a> page under the heading "Polar/Cylindrical Coordinates" for some references which I got on this forum a few days back.
  Reply With Quote

Old   May 29, 2003, 14:03
Default Re: singularity problem in cylindrical coordinate
  #3
Peter Rozovski
Guest
 
Posts: n/a
For Euler and Navier-Stokes equations in cylindrical case we have source term which is proportional to v/r. At r=0 this is avoidable singularity point 0/0 (v=0 at r=0). One widely used approach is to replace v/r at r=0 by dv/dr.
  Reply With Quote

Old   May 29, 2003, 14:12
Default Re: singularity problem in cylindrical coordinate
  #4
dallybird
Guest
 
Posts: n/a
Peter,

I dont quite understand, why v=o at r=0? if the cylinder is symmetric, dv/dr = 0 makes sense to me. can you give me some reference?
  Reply With Quote

Old   May 29, 2003, 16:03
Default Re: singularity problem in cylindrical coordinate
  #5
Peter Rozovski
Guest
 
Posts: n/a
In Euler & N-S case after change of coordinate system we have source term which is like nu*V*RO/r, where nu=0 for plane case and nu=1 for axi-symmetrical case (V is Y velocity and ro - density). In plane case nu=0 and we have no singularity. For axisymmetrical case by symmetry condition V=0 for r=0. So we can replace v/r = dv/dr / dr/dr = dv/dr. I am not sure where it was published, but when I was busy with CFD, it was usual approach. Probably you can find something in Pirumov, UG, Roslyakov, GS, "Gas Flow in Nozzles",Springer-Verlag, Berlin, 1986, but in reality the idea is all here.

  Reply With Quote

Old   June 2, 2003, 07:46
Default Re: singularity problem in cylindrical coordinate
  #6
zouchu
Guest
 
Posts: n/a
Verzicco & Orlandi have implemented a excellent finite difference method using staggered mesh and q1=V_t, q2=r*V_r, q3=V_z to handle the singularity of r=0. The recent book of Orlandi has the source code, and the reference J.C.P. paper is

c 1. R. Verzicco and P. Orlandi, "A finite-difference scheme for c three-dimensional incompressible flows in cylindrical coordinates", c J. Comput. Phys. 123, pp402-414, 1996.
  Reply With Quote

Old   June 3, 2003, 11:47
Default Re: singularity problem in cylindrical coordinate
  #7
Dayton
Guest
 
Posts: n/a
Look for a recent paper by LELE S.K. in Journal of Computational physics
  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
cylindrical to Cartesian coordinate bharath CFX 0 June 6, 2010 21:43
how to obtain velocity gradient on cylindrical coordinate rystokes CFX 1 March 3, 2010 00:47
change coordinate system cartesian to cylindrical tht FLUENT 0 September 6, 2007 05:46
IcoFoam parallel woes msrinath80 OpenFOAM Running, Solving & CFD 9 July 22, 2007 02:58
cartesian to cylindrical coordinate UDF Manoj FLUENT 0 December 15, 2005 10:43


All times are GMT -4. The time now is 22:57.