# Governing Equations of Fluent

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 March 25, 2017, 11:10 Governing Equations of Fluent #1 New Member   Join Date: Mar 2017 Posts: 1 Rep Power: 0 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.

 March 25, 2017, 16:49 #2 New Member     Steven Taggart Join Date: Jan 2014 Location: Hull, UK Posts: 25 Rep Power: 5 Hello, The i and j belong to vector notation being used, there are many good sources that will explain this better than me so I will let you look them up, any book on vector calculus will do, I used one by P.C.Mattews, it gave a good introduction to vector calculus. https://www.amazon.co.uk/Vector-Calc.../dp/B00FC7TW3C You could probably find a PDF of that book online but I'm not encouraging that ! The other variables have been omitted for clarity, the equations for the y and z axis will be identical to the ones shown for x but with the components changed to suit! Hope that helps! Steven

 March 26, 2017, 02:41 #3 Senior Member   Lucky Tran Join Date: Apr 2011 Location: Orlando, FL USA Posts: 1,880 Rep Power: 26 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). oozcan likes this.

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