- **Main CFD Forum**
(*http://www.cfd-online.com/Forums/main/*)

- - **Tensor Notation
**
(*http://www.cfd-online.com/Forums/main/5112-tensor-notation.html*)

Tensor Notation
Here is the problem:
T_ij = S_ij - .3*S_kk + S_ik*S_kj-.3*S_kl*S_kl The first term is i=1,j=1,k=1 T_11 = S_11 -.3(S_11+S_22+S_33) + S_11*S_11 - .3*(?) What do I do with this kl. I am trying to implement the explicit algebraic stress model, one could argue that if I can't figure out the tensor notation then I shouldn't be trying to implement an EASM model but that is just one of many problems. Thank You, Kevin |

Re: Tensor Notation
(?) = S11*S11+S12*S12+S13*S13
+ S21*S21+S22*S22+S23*S23 + S31*S31+S32*S32+S33*S33 It's the same for any ij. Was not it written S_kl*S_lk ? Which is the same if S is symetric, |

Re: Tensor Notation
hi kevin.
if i understand your question......... T_ij = S_ij - (S_kk) + [S_ik*S_kj] - {S_kl*S_kl} you understood the first bracketed term ( ) was an implied sumation. well the second bracketed term [ ] is also an implied summation on k. so you get = S_i1*S_1j + S_i2*S_2j + S_i3*S_3j and, the third term { }. this has a double repeated index, l and k and so you sum on both. giving = S_11*S_11 + S_12*S_12 + S_13*S_13 + S_21*S_21 + S_22*S_22 + S_23*S_32 + S_31*S_31 + S_32*S_32 + S_33*S_33 H. |

Re: Tensor Notation
Kevin,
The expression T_ij = S_ij - .3*S_kk + S_ik*S_kj-.3*S_kl*S_kl is not tensorially consistent because there are scalars (2ns and 4th terms on the right) mixed in with tensors (other terms). A correct form would be T_ij = S_ij - (.3*S_kk) delta_ij + S_ik*S_kj - (.3*S_kl*S_kl) delta_ij Terms involving repeated indices (k and l) have an implicit double summation. |

Re: Tensor Notation
Thank You all for you help with my Tensor Notation and also catching my two mistakes, not summing the second term and leaving out the delta_ij function.
Now time to have fun solving this equaiton. Kevin |

All times are GMT -4. The time now is 08:46. |