# boundary condition for streamline func and vorticity

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June 16, 2018, 12:24
boundary condition for streamline func and vorticity
#1
Senior Member

A. Min
Join Date: Mar 2015
Posts: 305
Rep Power: 12
Hi all
I have a solved domain (2D flow around a circular cylinder) with U field. Now I want to calculate stream function with this formulation:
Code:
```omega = dv/dx - du/dy
solve (laplacian (sai) = - omega)```
But at last the results are wrong!
The BC for sai are:
for top and bottom sai is calculated from the volumetric flux (Q = A.U_in) that is:
Quote:
 sai_top - sai_bottom = U*delta(y) = 1*20 = 20, so: top boundary: sai = 10 bottom boundary: sai = -10 cylinder surface boundary: sai = 0 inlet and outlet boundaries: d(sai)/dn = 0
and for omega:

Quote:
 top, bottom, outlet boundaries: zero Gradient inlet and cylinder : omega = 0
But the constant sai lines are not the same as stream lines:

Could you please help me?

Are the equations and boundary C. correct?

June 16, 2018, 13:08
#2
Senior Member

Santiago Lopez Castano
Join Date: Nov 2012
Posts: 354
Rep Power: 15
Quote:
 Originally Posted by alimea Hi all I have a solved domain (2D flow around a circular cylinder) with U field. Now I want to calculate stream function with this formulation: Code: ```omega = dv/dx - du/dy solve (laplacian (sai) = - omega)``` But at last the results are wrong! The BC for sai are: for top and bottom sai is calculated from the volumetric flux (Q = A.U_in) that is: and for omega: But the constant sai lines are not the same as stream lines: Could you please help me? Are the equations and boundary C. correct?
If bottom and top are also walls, they should be zero as well. The inlet BC in principle a distribution of psi if the inlet is nonuniform. Otherwise the formulation seems correct to me. Btw, why do you expect to get the same results?

June 16, 2018, 13:12
#3
Senior Member

A. Min
Join Date: Mar 2015
Posts: 305
Rep Power: 12
Quote:
 Originally Posted by Santiago If bottom and top are also walls, they should be zero as well. The inlet BC in principle a distribution of psi if the inlet is nonuniform. Otherwise the formulation seems correct to me. Btw, why do you expect to get the same results?
Thanks Santiago to reply.

top and bottom are p=0 boundaries.
I have tested this boundary for inlet, this is the same as linear distributed sai.

About your question:
"why do you expect to get the same results?"

constant stream function is the same as stream line, isn't it?!

If not, could you please tell me why?

 Tags boundary condition, streamline, vorticity

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