Flow over a backwards facing step is a classic computational fluid dynamics test problem which is used extensively for validation of simulation codes. The test problem essentially consists of studying how a fully developed flow profile reacts to a sudden expansion in a channel. The expansion will cause a break in the flow and a recirculation or separation zone will form. To measure and compare results the resulting length of the recirculation or separation zone is used.

The stationary incompressible Navier-Stokes equations are applied with
simulation parameters corresponding to a Reynolds number, *Re =
389*. The inlet velocity is given as *u _{inlet} = 4u_{max}
(y-h_{step})(1-y)/h_{inlet}^{2}* where

*h*is the channel height,

_{inlet}*hstep*the expansion step height, and

*u*the maximum velocity. No-slip zero velocity conditions are applied to all solid walls, and a suitable outflow condition must also be applied. The reference recirculation zone length found in the references [1], [2] is estimated to be

_{max}= 1*7.93*length units (fraction of the step height).

This model is available as an automated tutorial by selecting **Model Examples and Tutorials…** >
**Fluid Dynamics** > **Flow Over a Backwards Facing Step**
from the **File** menu, and also as the MATLAB simulation m-script example ex_navierstokes4.
Step-by-step tutorial instructions to set up and run this model are linked below.

## References

[1] P.M. Gresho and R.L. Sani, Incompressible Flow and the Finite Element Method, Volume 1 & 2, John Wiley & Sons, New York, 2000.

[2] A. Rose and B. Simpson: Laminar, Constant-Temperature Flow Over a Backward Facing Step, 1st NAFEMS Workbook of CFD Examples, Glasgow, UK, 2000.