Backward Facing Step Flow
 

Hello to everyone
I've written a code to simulate laminar backward facing step flow. The main features of the method I have developed are as follows:
- incompressible flow
- finite volume
- Simple algorithm on Staggered grids
- 1st order Upwinding for convection terms
- central differencing for diffusion terms
- Iterative solution to obtain steady solution (no time marching)
- using line TDMA for the solution of algebraic equations of x-y momentum and pressure correction
at lower Reynolds numbers the code works satisfactorily but at higher Reynolds numbers (e.g. 600, 800) the L2 norm of mass unbalance decreases 1 or 2 order of magnitudes, then it oscillates but doesn't decrease further.
I have checked the Residuals, the cells where the mass unbalance doesn't decrease, are located near the end of lower wake.
I have tested the code for simulating cavity driven flow, it works fine.
Does anybody have any suggestion? What shall I do? Does the flow have unsteady nature at high Reynolds numbers?

yes, after Re=700- 800 the flow is transitional and it has no sense the 2D laminar solution. You can search for a paper of Armaly et al. on JFM

For Re=600, 800 the flow is not anymore steady and is definitely unsteady.
So it is normal that your code can not find a steady solution of a flow which is unsteady.

So implement unsteady version of your solver accounting for time derivative.
refine the grid because you increase the Reynolds and re-run it,it should be fine.

Thanks a lot
I have another question regarding the flow over a backward step:
How can I calculate the reattachment region length?

The reattatchment point is usually defined by the position where the wall shear stress (its streamwise component) changes sign.