External forces in Navier-Stokes equation

General Discussion
1

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!