Model 2D Incompressible Fluid w/ Navier-Stokes Equations

[Zhivago]

Hello everyone

I'm for the first time trying to model using the Navier-Stokes equations.
I want to model a 2D problem where I have an incompressible, non viscous fluid. I have a region (a segment of line) where a force is applied to the fluid.
For example: a rectangular box with size 2L x L. In a line at x=L (or some other point) with height (L/4) a constant force is applied to the fluid.
How could I model this?

I suppose I could use the static regime, and model this force as a pressure gradient at the line?
But how?

setting /rho = 1, and assuming the solution doesn't depend on time,

v . grad(v) = - grad (p)

is this a good way to go? what can I do with this equation? Should I use the force term in the equation instead of a pressure gradient?
I would say this problem is similar to having 2 close conducting plates (or lines) with opposite charges and finding the electric field / current density.

Any thoughts / ideas?

 

[genneth]

The problem is incomplete without specifying boundary conditions: i.e. what lies outside of the region you're considering.

 

[Zhivago]

Oh yes, of course. The walls are fixed at x = 0, 2L and y = 0, L

The walls are fixed, no fluid going through them. All velocities start at 0.

If the velocity is (u, v), I should have a system of equations

<br /> u u_x + v u_y = -p_x<br />

<br /> u v_x + v v_y = -p_y<br />

<br /> u_x + v_y = 0<br />

the indices represent derivative

(the last equation from div(velocity) = 0)

Would this tackle the problem somehow? But how to set the initial force / pressure?