Adding U*U as a source term
I am trying to solve the following equation:
dU/dt = grad(p) - 0.5*(f/L)*(U*U)
here, U(velocity vector), p (pressure), and L is length, (f is dimensionless scalar).
In fact, I made an attempt and it seems working for 1D .. However, I can not be very sure about the approach that I use (especially for 2D and 3D problems), and I need some comments from more experienced people.
I constructed my equations as follows:
Instead, assuming that only the i component of the vectors will be used while solving Ux, I wrote "U & identity" to obtain the value of the x component of U and put it in to the first parameter place of Sp function.
This works for 1D but I cannot be sure about my assumption about the behavior of U & identity expression in 2D and 3D problems..
In short, say that U(1, 2, 3) then will "U & identity" produce 1+2+3=6 in ALL Ux, Uy and Uz solutions OR will it produce 1 in Ux solution, 2 in Uy solution and 3 in Uz solution??
PS: The above is not a realistic CFD problem, but I am just playing a little with the code so to get some understanding...
Anyway, I think I got the answer of my question by constructing a 2D case. And, I saw that unfortunately (in fact fortunately) my assumption was wrong, i.e. use of "U & identity" produced Ux+Uy+Uz.
So, in this problem, what is needed is something like scale(U,U) function, which gives the product of corresponding components of vectors U and U; so it will produce another vector (not a matrix which only the main diagonal is useful).
I couldn't still make scale(U,U) work. But asked about it under another title.
scale(U,U) doesn't work and unfortunately it has not been updated in programmers guide. You should use cmptMultiply(U,U) instead.
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