backward_step

backward_step, a FreeFem++ code which solves the backward step benchmark problem for Navier Stokes flow.

The backward step geometry is:

  | y=H   +--------------L5--------+  y=H
  |       |                        |
  |       L1                       L2
  |       |                        |
  | y=0.5 +-L4--+                  |
  |             L4                 |
  | y=0         +--------L3--------+  y=0
  |       ^     ^                  ^
  |       x=0   x=3                x=22
  |
  +--------------------------------------------------

In flow case 1, H = 1.5, and in flow case 2, H = 1. Solutions are desired at Reynolds numbers 50, 150, 500. Side L1 is an inflow boundary, with a parabolic inflow profile: uinflow = (H-y)*(y-1/2)/((H-1/2)/2)^2

Side L2 is an outflow boundary where boundary conditions are not imposed. Sides labeled L3, L4 and L5 are no slip walls, with U = V = 0. The steady incompressible Navier Stokes equations for (u,v,p) in 2D are:

  -nu ( uxx + uyy ) + u ux + v uy + px = 0
  -nu ( vxx + vyy ) + u vx + v vy + py = 0
                               ux + vy = 0

where nu is the kinematic viscosity.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license.

Reference:

Frederic Hecht, New development in FreeFem++, Journal of Numerical Mathematics, Volume 20, Number 3-4, 2012, pages 251-265.

Source Code:

• backward_step.edp, the FreeFem++ script;
• backward_step.sh, a BASH script to run the example;
• backward_step.txt, the output file;
• backward_step_mesh.png, a PNG image of the mesh;