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Computational fluid dynamics: steady 2D flow

  1. Mar 10, 2015 #1
    1. The problem statement, all variables and given/known data
    cfd.png

    2. Relevant equations
    CFD

    3. The attempt at a solution
    I'm a bit confused by this question.

    So at first what I do for the problem on the left, I find the changes in the velocities in X and and Y on all four sides.

    I notice that the values on the diagram to the left are higher on top than they are on the bottom, therefore I conclude that v must be "up".
    I also notice that the values are higher on the right than they are on the left, therefore I conclude that u is to the right.

    For the diagram on the right: I notice that bottom > top, therefore v is down.
    Right > left, therefore u is to the right.


    Are these assumptions correct?

    After that it's a fairly simple problem but this first step has me confused as to what I'm supposed to be doing.
     
  2. jcsd
  3. Mar 10, 2015 #2
    I think what they want you to do is to find the y velocity components at the centers of the horizontal faces, and the x velocity components at the centers of the vertical faces, and then average to get the velocity components at the center of the cell.

    Chet
     
  4. Mar 10, 2015 #3
    I don't understand. The solution says "Ψtop>Ψbottom, therefore U is to the right" and "Ψright>Ψleft therefore V is down".
    This is completely counter intuitive and seems to be taken out of the thin air. What are they basing this on?
     
  5. Mar 10, 2015 #4
    $$v_x=\frac{\partial \psi}{\partial y}$$
    $$v_y=-\frac{\partial \psi}{\partial x}$$
     
  6. Mar 10, 2015 #5
    That makes a million times more sense. Thanks.
     
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