# External forces in Navier-Stokes equation

**URL:** https://community.freefem.org/t/external-forces-in-navier-stokes-equation/965
**Category:** General Discussion
**Created:** [May 7, 2021, 9:24am UTC](https://community.freefem.org/t/external-forces-in-navier-stokes-equation/965 "2021-05-07T09:24:57Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![yhao](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@yhao](https://community.freefem.org/u/yhao)
#### Post date: [May 7, 2021, 9:24am UTC](https://community.freefem.org/t/external-forces-in-navier-stokes-equation/965/1 "2021-05-07T09:24:57Z")

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Hi,

I am trying to solve the Navier-Stokes equations with an external force that is perpendicular to the velocity. Firstly I defined a fespace of it and made function f on the fespace:

> ```
> fespace Fh(Th, P2dc);
> Fh fu = k*u, fv = k*v;
> 
> ```

k is defined on a P0 fespace, and u and v are the velocity defined on a P2 fespace. When I included it in the Navier-Stokes equation and solved it, it would show that “velocity too high”, and got a wrong value.

> ```
> problem navierstokes ( [u, v, p], [uh, vh, ph]) = int2d(Th) ( rho * u * uh / dt )
> - int2d(Th) ( rho * convect ([uold,vold], -dt, uold) * uh / dt )
> + int2d(Th) ( rho * v * vh / dt )
> - int2d(Th) ( rho * convect ([uold,vold], -dt, vold) * vh / dt )
> + int2d(Th) ( nu * dx(u) * dx(uh) + nu * dy(u) * dy(uh) )
> + int2d(Th) ( nu * dx(v) * dx(vh) + nu * dy(v) * dy(vh) )
> + int2d(Th) ( fu * uh)
> + int2d(Th) ( fv * vh)
> - int2d(Th) ( p * dx(uh) )
> - int2d(Th) ( p * dy(vh) )
> + int2d(Th) ( dx(u) * ph + dy(v) * ph )
> - int1d(Th, c4) ( nu * dx(u) * N.x * uh + nu * dy(u) * N.y * uh )
> - int1d(Th, c4) ( nu * dx(v) * N.x * vh + nu * dy(v) * N.y * vh )
> + on ( c1, c3, u=0.0, v=0.0 )
> + on ( c4, u=uin, v=0);
> 
> ```

But when I directly included k\*u in the Navier-Stokes equation, it can run the simulation.

> ```
> + int2d(Th) ( k * u * uh)
> + int2d(Th) ( k * v * vh)
> 
> ```

Can I ask why there is this problem? And what I can do if I want to use the fespace function for the force?

Thanks in advance!