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

pointcare index

Register Blogs Community New Posts Updated Threads Search

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   November 1, 2004, 01:29
Default pointcare index
  #1
autofly
Guest
 
Posts: n/a
hi I meet difficulty in understanding the definition of pointcare index. when study the topotical structure on surface. the sum of saddle and nodal points must meet certain relationship. for a common case.sum( N) -sum(S) = 2 but for special case sum(N) + 1/2 sum(N')- sum(S) - 1/2 sum(S')= I

I is the pointcare index. how to get it?

in a formula I = D-phi/2*pi, i dong't know how to get the phi? who can give me detailed intepretation? thanks
  Reply With Quote

Old   November 6, 2004, 23:57
Default Re: Poincare index
  #2
versi
Guest
 
Posts: n/a
Your first formula is right , but your second formula about relation of Poincare indices in 2D should be sum(N) + 1/2 sum(N')- sum(S) - 1/2 sum(S')= -1 , where N is a full node or focus point or center point, S is a full saddle point, N' or S' are half node (saddle) point on the boundary of the 2D domain. The index of a full node = 1 while the index of a saddle =-1, the index of a node (saddle) on the boundary is counted as 1/2 (-1/2). The meaning of Poincare Index can be found in many text books about topology and dynamic theory. If you draw a closed loop around a critical point and monitor the direction change of the unit field vetor along this loop counterclockwise, if change of the direction of the unit field vector is counterclock +360 (or -360) deg , then Poincare index =+1 (or -1).

  Reply With Quote

Old   November 8, 2004, 14:32
Default Re: pointcare index
  #3
Nicola
Guest
 
Posts: n/a
For a general surface, the sum(N)-sum(S)=2-2*g=I where g is the number of holes in the surface. So, for the flow over a sphere I=2, for the flow over a thorus I=0.

Hope it helps,

Nicola
  Reply With Quote

Reply


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
gamma-ReTheta turbulence model for predicting transitional flows FelixL OpenFOAM Programming & Development 123 August 30, 2022 12:50
centricity index, uniformity index LeonardLapis Main CFD Forum 5 August 27, 2015 00:46
Doxygen documentation Tanay OpenFOAM Installation 9 September 23, 2011 12:40
OpenFOAM install on Ubuntu Natty 11.04 bkubicek OpenFOAM 13 May 26, 2011 06:48
Dryden index fjalil Main CFD Forum 0 July 7, 2010 12:33


All times are GMT -4. The time now is 05:25.