[mo.almuqbel]

Hello Everyone!

Perhaps its a very trivial question, but can someone please point out on what does the little "i" and "j" mean when they are associated as a subscript to x and u in the following slide? Also I am a bit confused on why there is no mention of the other variables such as v, w and y and z.

https://image.slidesharecdn.com/cfx1...?cb=1428161029
I really appreciate your help.

[LuckyTran]

It's tensor subscript notation.

u is the entire velocity vector (i.e. u = [u_x,u_y,u_z], not one of its directional components. Same thing with x. This way u_i refers to the individual components and x_i refers to the individual components. The v,w,y,z are not omitted per se, it's just that u and x mean something else. If you want you can replace u and x by another symbol like U and X if you want to make the distinction so that U = [Ux,Uy,Uz] and X = [x,y,z]

u_i means to loop over i or take all its permutations. Pay attention to two different symbols, if they have the same subscript or not (i & i or i & j).