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Simple Navier-Stokes

  1. Sep 30, 2011 #1
    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?
  2. jcsd
  3. Sep 30, 2011 #2
    The problem is incomplete without specifying boundary conditions: i.e. what lies outside of the region you're considering.
  4. Sep 30, 2011 #3
    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

    u u_x + v u_y = -p_x

    u v_x + v v_y = -p_y

    u_x + v_y = 0

    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?
    Last edited: Sep 30, 2011
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