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-   -   How to calculate these tensor term ? (http://www.cfd-online.com/Forums/main/8271-how-calculate-these-tensor-term.html)

Nokadu October 28, 2004 01:51

How to calculate these tensor term ?
 
There is 2 tensor that i don,t know how to calculate! 1: S_ij*S_ij = ?

2: S_ij*S_jk*S_ki= ?

there : i=1,2,3,j=1,2,3 Who can give me an exact formula about these calculations (in terms S_11,S_12,....)??

thaks!

Praveen October 28, 2004 03:27

Re: How to calculate these tensor term ?
 
Repeated indices imply summation. So

S<sub>ij</sub> S<sub>ij</sub> = &Sigma;<sub>i</sub> &Sigma;<sub>j</sub> S<sub>ij</sub> S<sub>ij</sub>

which is a scalar.

John Luo October 29, 2004 06:59

Re: How to calculate these tensor term ?
 
If you have S11=2.*DU/DX, S22=2.*DVDY, S33=2.*DW/DZ, S12=DUDY+DVDX, S23=DV/DZ+DW/DY, S31=DW/DX+DU/DZ,

THEN SIJ*SIJ=S11**2+S22**2+S33**2+2.*(S12**2+S23**2+S31 **2)

SIJ*SJK*SKI=S11**3+S22**3+S33**3+6.*S12*S23*S31+ 3.*[S12**2*(S11+S22)+S23**2*(S22+S33)+S31**2*(S33+S11)]


Nokadu October 29, 2004 14:48

Re: How to calculate these tensor term ?
 
Thank you 2 very much!

In chinese : ллǣdzл


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