# Boundary conditions of stream function

I have to do an problem about solving numerically the flow that goes under an airfoil. The airfoil has a flap deployed downwards and I need to solve the mesh that it's under the airfoil.

I have drawn the scheme of the problem which is the following:

I need to compute the values of stream function ( $\psi$), velocity (x and y components) and pressure coefficient at every node of the mesh (every node is a blue dot). the spacing between them is 0.1m on the x-direction and on the y-direction.

In order to compute stream function I have to discretize the Laplace equation: $$\dfrac{\partial^2 \psi}{\partial x^2} + \dfrac{\partial^2 \psi}{\partial y^2} = 0$$

However, I don't know what boundary conditions for stream function I must set in order to obtain 30 m/s at the left-hand side, and 60 m/s at the right-hand side.

I did the problem once but I mistook in the result because of the $\psi$ boundary conditions. So, I need to know what they would be on the upper wall, at the entrance (left side), at the exit and at the lower part (free stream). Or you could told me how to compute them at every part.

• Related by OP: physics.stackexchange.com/q/154252 – Kyle Kanos Dec 20 '14 at 18:36
• Looks like Dirichlet boundaries at (1,:) and (16,:) for the velocities. How do those relate to $\psi$? – Kyle Kanos Dec 20 '14 at 18:38
• I'm not really sure, but could it be a linear variation? @KyleKanos – user3780731 Dec 20 '14 at 19:34
• The question meant to ask, How do the velocities, $u,\,v$, relate to $\psi$? This is a straight-forward definition that you should know immediately. If not, you need to go back to your textbook and find the answer. – Kyle Kanos Dec 20 '14 at 19:40
• Do you know what boundary conditions are? Really not trying to be glib, but @KyleKanos gave you literally everything you need in his comment. And your response contains everything you need. – tpg2114 Dec 20 '14 at 20:09