
[Sponsors] 
October 4, 2012, 12:39 
Simple vector notation help. uiuj in non index notation

#1 
Member
Casey
Join Date: Jun 2009
Posts: 96
Rep Power: 8 
Hey Everyone,
For my paper I have about 50 equations all in the "standard" vector notation , but there are 2 or 3 turbulence equations with the Reynolds stress therm in index notation that I don't know how to put in the "standard form". The term is below: = ??? in standard form I think is not correct or at least will make the reader think I am talking about the dot product of u with u. 

October 4, 2012, 12:48 

#2 
Member
Casey
Join Date: Jun 2009
Posts: 96
Rep Power: 8 

October 4, 2012, 13:01 

#3 
Senior Member
Join Date: Jul 2009
Posts: 207
Rep Power: 9 
If you are referring to the terms in the Reynolds stress tensor, your friend is correct. The term for such a representation is dyadic.


October 4, 2012, 13:11 

#4 
Member
Casey
Join Date: Jun 2009
Posts: 96
Rep Power: 8 

October 4, 2012, 16:34 

#5 
Senior Member
Join Date: Jul 2009
Posts: 207
Rep Power: 9 
They are not the same thing. The outer product of two vectors is another vector. The inner product of two vectors is, of course, a scalar. The dyadic product of two vectors is a tensor of order 2 (since the vectors are each tensors of order 1). When you write the index notation (ui)(uj) without any caveats, it generally implies the dyadic product.


October 5, 2012, 10:23 

#6 
Member
Casey
Join Date: Jun 2009
Posts: 96
Rep Power: 8 
I just looked and according to wiki (i know, i know) the outer product does produce a tensor. Are you sure about your answer?


October 7, 2012, 11:05 

#7 
Senior Member
Chris DeGroot
Join Date: Nov 2011
Location: Canada
Posts: 387
Rep Power: 7 

October 7, 2012, 11:07 

#8 
Senior Member
Join Date: Jul 2009
Posts: 207
Rep Power: 9 
Sorry  I saw the symbol and my brain interpreted it as the cross product. Yes, the outer product results in the same thing as the dyadic product. It is not the same thing as the cross product, which produces a tensor of the same order as the original entries.


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
gammaReTheta turbulence model for predicting transitional flows  FelixL  OpenFOAM Programming & Development  79  October 11, 2015 15:30 
FvMatrix coefficients  shrina  OpenFOAM Running, Solving & CFD  10  October 3, 2013 14:38 
Doxygen documentation  Tanay  OpenFOAM Installation  9  September 23, 2011 11:40 
OpenFOAM install on Ubuntu Natty 11.04  bkubicek  OpenFOAM  13  May 26, 2011 05:48 
Notation Standards and Uniformity  yNot  CFDWiki  0  April 5, 2008 15:00 