Impose a gradient boundary condition

Hello everyone,

Recently, I have been working on solving \Delta \phi = 0. Here, \phi is the potential of speed (so v = \nabla \phi) in a fluid, around a cylinder (so there is a z-invariance to the problem and it can be solved in 2D). Because I work on a visquous fluid, I would like the speed around the cylinder to be equal to zero, so \frac{\partial \phi}{\partial x} = \frac{\partial \phi}{\partial y} = 0. How could I do this, knowing that I solve this problem :


The boundary conditions on the square borders are that the speed is e_y, hence the int1d that appears in the Laplacian problem.
Thanks in advance to anyone trying to help me.

ps : Here you can see the solution \phi

and the field of speed

Your equation is for potential flow of an inviscid fluid. You cannot enforce those constraints on inviscid flow.