# Normal to the boundary

**URL:** <https://community.freefem.org/t/normal-to-the-boundary/1339>\
**Category:** General Discussion\
**Created:** [November 19, 2021, 6:51am UTC](https://community.freefem.org/t/normal-to-the-boundary/1339 "2021-11-19T06:51:32Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![zese](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/zese/32/917_2.png) [@zese](https://community.freefem.org/u/zese)\
**Post date:** [November 19, 2021, 6:51am UTC](https://community.freefem.org/t/normal-to-the-boundary/1339/1 "2021-11-19T06:51:33Z")

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Dear all,

I want to specify a blowing on airfoil wall as v\_j=v.n\_w in which n\_w is the normal to the airfoil. How this normal can be defined?. Is N.y for normal to the boundary or it is just a unit vector in y direction?

best regards,

Zeinab

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**Author:** ![UgisL](https://avatars.discourse-cdn.com/v4/letter/u/c0e974/32.png) [@UgisL](https://community.freefem.org/u/UgisL)\
**Post date:** [November 19, 2021, 9:50am UTC](https://community.freefem.org/t/normal-to-the-boundary/1339/2 "2021-11-19T09:50:30Z")

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Hi Zeinab,

in FreeFEM, N.x and N.y on the boundaries are x and y components of the surface normal vector. Note that as per standard convention, the normal vector points outside of the defined domain.

I hope this helps.

Best,  
Ugis

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<div class="post-metadata">

**Author:** ![zese](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/zese/32/917_2.png) [@zese](https://community.freefem.org/u/zese)\
**Post date:** [November 19, 2021, 10:01am UTC](https://community.freefem.org/t/normal-to-the-boundary/1339/3 "2021-11-19T10:01:12Z")

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Dear Ugis

Thank you for your response. for example for my case as the figure below, I have the following expression:  
V\_j=u_N.x+v_N.y ? because I had V\_j=|V\_j|.n  
so now I have two components which should be specified. do I need to find the tangent to the surface and find a relation between u and v to diminish the unknowns?

![2021-11-18_11-49-28](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/1X/8f3d7567405aba29a6619aeaf607840f6a23f57d.jpeg)

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**Author:** ![UgisL](https://avatars.discourse-cdn.com/v4/letter/u/c0e974/32.png) [@UgisL](https://community.freefem.org/u/UgisL)\
**Post date:** [November 19, 2021, 10:05am UTC](https://community.freefem.org/t/normal-to-the-boundary/1339/4 "2021-11-19T10:05:46Z")

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Indeed, that could be needed in some cases. But only if you need to also impose tangential velocity.

But this is up to your specification of the problem and not that much about the solver code … In general, for interface normal velocity only with magnitude U, in vector form you would have vec{u} = U\*(N.x+N.y). Consequently, x component is U_N.x and y component is U_N.y.

/Ugis