k-e equation in in cartesian coords
 

Hi,

I'm trying to expand the k-epsilon equations from cartesian tensor notation to cartesian coordinates to form a system of equations for finite element analysis.

Both the k- and e-equations contain a term with the Reynolds stresses expressed as follows:

( @Ui/@Xj + @Uj/@Xi ) ( @Ui/@Xj)

Does this represent a scalar quantity (ie the scalar product of the two tensors), or a 3x3 matrix product in 3D?

Thanks in advance, -CS

Re: k-e equation in in cartesian coords
 

Any term in k and e equations is scalar because k and e themselves are scalars.

Re: k-e equation in in cartesian coords
 

What you are looking at is part of the production term in k and eps-equation, which are - yes a scalar. However in order to compute the production term you need to cycle through i and j indices from 1 to 3, hence the expression becomes something like:

P_k=\nu_t((dU/dy+dV/dx)dU/dy+(dU/dz+dW/dx)dU/dz+....

/Jonas