# Developing region plane Poiseuille Flow: problem Inlet BC **URL:** \ **Category:** General Discussion\ **Created:** [January 20, 2025, 8:30pm UTC](https://community.freefem.org/t/developing-region-plane-poiseuille-flow-problem-inlet-bc/3697 "2025-01-20T20:30:27Z")\ **Posts on this page:** 2\ **Page:** 1
**Author:** ![lparras](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/lparras/32/544_2.png) [@lparras](https://community.freefem.org/u/lparras)\ **Post date:** [January 20, 2025, 8:30pm UTC](https://community.freefem.org/t/developing-region-plane-poiseuille-flow-problem-inlet-bc/3697/1 "2025-01-20T20:30:27Z")
Dear all. I have developed a 2D flow to solve the steady NS equations for a more complicated mesh. Once I got the code working, I have tried to test it against some analytic problem. I have used the developing region of plane Poiseuille flow (x \in[0,L] and y \in [0 H]). The inlet boundary condition is u1 = 1, u2=0, the upper and lower walls are non slip. I solve the steady problem using Newton-Raphson and once I got the results, I have realised that the inlet boundary condition is slightly modified (it is not really imposing Ux=1). I send you here a plot ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/4/4fd308dfa89b8ddc2f20f4a799ad556924b9bea9.png) I upload a test problem. The results are written in datosPlanePoiseuille.dat, where the first column is the coordinate y, the second column u1(x=0) and the third one u1(x=L). You can see that there is an overshoot near the walls at the inlet boundary condition whereas I would expect to have u1 = 1. [testSteadyNSplanePoiseuille.edp](https://community.freefem.org/uploads/short-url/jcDSx3j7ZM8FBjJoLW5lTRJUu9l.edp) (4.8 KB) ---
**Author:** ![fb77](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/fb77/32/3796_2.png) [@fb77](https://community.freefem.org/u/fb77)\ **Post date:** [January 21, 2025, 1:11pm UTC](https://community.freefem.org/t/developing-region-plane-poiseuille-flow-problem-inlet-bc/3697/2 "2025-01-21T13:11:35Z")
Your problem is discretized with 20 intervals in the `y` direction, but you plot 100 values of y. It follows that the points that you plot on the boundary are just interpolation of the values 0 and 1. If in your code you take `nl = 21` then the .dat file is correct: 0 -2.683e-32 4.91667e-34 0.05 1 0.28025 0.1 1 0.531 0.15 1 0.75225 0.2 1 0.944 0.25 1 1.10625 0.3 1 1.239 0.35 1 1.34225 0.4 1 1.416 0.45 1 1.46025 0.5 1 1.475 0.55 1 1.46025 0.6 1 1.416 0.65 1 1.34225 0.7 1 1.239 0.75 1 1.10625 0.8 1 0.944 0.85 1 0.75225 0.9 1 0.531 0.95 1 0.28025 1 -2.65432e-32 4.91667e-34 The left corners are set to 0 because you impose 0 on upper and lower boundaries. Note that the order in which you set the BC matters: + on(inlet, up1=1, up2=0) + on(upperWall, up1=0,up2=0) + on(lowerWall, up1=0, up2=0) + on(outlet,up2=0) On the left corners you have two definitions of up1 : inlet and upper/lower wall. The one that is applied is the last one in the list: up1=0. If you change the order, as + on(upperWall, up1=0,up2=0) + on(lowerWall, up1=0, up2=0) + on(inlet, up1=1, up2=0) + on(outlet,up2=0) Then the left corners take the value up1=1.