Einestine summation - help
 

Can someone explain to me which one of this is right for;

d(u_i u_i)/dt = nu(d(u_i)/d(x_j))^2

for x - momentum

is it

A. d(u_1)^2/dt = nu(d(u_1)/d(x_1) + d(u_1)/d(x_2))^2

or

B. d(u_1)^2/dt = nu(d(u_1)/d(x_1))^2 + (d(u_1)/d(x_2))^2.

I am really confused, please help.

With regards,

Tilek

Re: Einstein summation - help
 

With Einstein Summation, you will only sum over the repeated index (indices), (i.e. 'i' in this case)

For X-momentum (j=1) you would sum the i's (i=1,2,3)

But since this sounds like a homework assignment I won't put up the answer just yet.

Re: Einestine summation - help
 

Yeah thanks for the comment and I still look forward to your feedback.

A colleague here said it is (A). But I saw esp. the RHS to be possibly written as nu(d(u_i)/d(x_j))(d(u_i)/d(x_j)) in which case (B) looks the case applicable here. In my first thought also; if I have to write it in code (like Fortran), with a do loop, it sounds to be case (B). But in the line of the rule "sum first the repeated indices", it would look case (A) applies. I think this is a simple problem for those in turbulence research, which I am struggling right now. I appreciate feedback still.

Cheers, TAW

Re: Einestine summation - help
 

Well for strictly ESN (Einstein Summation Notation), both are wrong. You will not sum the J's, since it is not a repeated index, so leave the J as is.

And if you want just i=1, just substitute in. This isn't really ESN if you just want i=1.