[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:

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:

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:

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?

[Santiago]

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:

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?

[alimea]

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?